Adding and Subtracting Radicals - Algebra 2
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Subtract and simplify:
Subtract and simplify:
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Find the lease common denominator: 
A radical cannot be in the denominator:
Find the lease common denominator:
A radical cannot be in the denominator:
Solve.
Solve.
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When adding and subtracting radicals, make the sure radicand or inside the square root are the same.
If they are the same, just add the numbers in front of the radical.
Since they are not the same, the answer is just the problem stated.
When adding and subtracting radicals, make the sure radicand or inside the square root are the same.
If they are the same, just add the numbers in front of the radical.
Since they are not the same, the answer is just the problem stated.
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The third root of 
is 
and when added to the square root of 64, which is 8, you should get 11.
The third root of
and when added to the square root of 64, which is 8, you should get 11.
Find the value of 
.
Find the value of
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To solve this equation, we have to factor our radicals. We do this by finding numbers that multiply to give us the number within the radical.
Add them together:
4 is a perfect square, so we can find the root:
Since both have the same radical, we can combine them:
To solve this equation, we have to factor our radicals. We do this by finding numbers that multiply to give us the number within the radical.
Add them together:
4 is a perfect square, so we can find the root:
Since both have the same radical, we can combine them:
Simplify the following equation:
Simplify the following equation:
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When simplifying, you should always be on the lookout for like terms. While it might not look like there are like terms in 
, there are -- we just have to be able to rewrite it to see.
Before we start combining terms, though, let's look a little more closely at this part:
We need to "distribute" that exponent to everything in the parentheses, like so:
But 4 to the one-half power is just the square root of 4, or 2.
Okay, now let's see our equation.
We need to start combining like terms. Take the terms that include x to the one-half power first.
Now take the terms that have x to the one-third power.
All that's left is to write them in order of descending exponents, then convert the fractional exponents into radicals (since that's what our answer choices look like).
When simplifying, you should always be on the lookout for like terms. While it might not look like there are like terms in
Before we start combining terms, though, let's look a little more closely at this part:
We need to "distribute" that exponent to everything in the parentheses, like so:
But 4 to the one-half power is just the square root of 4, or 2.
Okay, now let's see our equation.
We need to start combining like terms. Take the terms that include x to the one-half power first.
Now take the terms that have x to the one-third power.
All that's left is to write them in order of descending exponents, then convert the fractional exponents into radicals (since that's what our answer choices look like).
Simplify.
Simplify.
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We can simplify both radicals:
and 
Plug in the simplified radicals into the equation:
which leaves us with:
Because these are not like terms, we cannot simplify this further.
We can simplify both radicals:
Plug in the simplified radicals into the equation:
which leaves us with:
Because these are not like terms, we cannot simplify this further.
Simplify.
Simplify.
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Only the first two radicals can be simplified:
and 
Plug in the simplified radicals into the equation:
We can now simplify the equation by combining the like terms:
Only the first two radicals can be simplified:
Plug in the simplified radicals into the equation:
We can now simplify the equation by combining the like terms:
Simplify.
Simplify.
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We can simplify the first and third radicals:
and 
Plug in the simplified radicals into the equation:
Combine the like terms:
We can simplify the first and third radicals:
Plug in the simplified radicals into the equation:
Combine the like terms:
Solve.
Solve.
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When adding and subtracting radicals, make the sure radicand or inside the square root are the same.
If they are the same, just add the numbers in front of the radical.
Since they are not the same, the answer is just the problem stated.
When adding and subtracting radicals, make the sure radicand or inside the square root are the same.
If they are the same, just add the numbers in front of the radical.
Since they are not the same, the answer is just the problem stated.
Solve.
Solve.
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When adding and subtracting radicals, make the sure radicand or inside the square root are the same.
If they are the same, just add the numbers in front of the radical.
Looking carefully at the radicand we will notice that each radicand is a perfect sqare. This means we are able to reduce the radical into an integer.
and 
are all sqaure numbers so instead we have a simple algebraic problem:
which the answer is 
.
When adding and subtracting radicals, make the sure radicand or inside the square root are the same.
If they are the same, just add the numbers in front of the radical.
Looking carefully at the radicand we will notice that each radicand is a perfect sqare. This means we are able to reduce the radical into an integer.
Solve.
Solve.
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When adding and subtracting radicals, make the sure radicand or inside the square root are the same.
If they are the same, just add the numbers in front of the radical.
Looking carefully at the radicand we will see that each radicand is a perfect square. Therefore, we are able to reduce all of the radicals into simple integers.
and 
are all sqaure numbers so instead we have a simple algebraic problem:
which the answer is 
.
When adding and subtracting radicals, make the sure radicand or inside the square root are the same.
If they are the same, just add the numbers in front of the radical.
Looking carefully at the radicand we will see that each radicand is a perfect square. Therefore, we are able to reduce all of the radicals into simple integers.
Solve.
Solve.
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When adding and subtracting radicals, make the sure radicand or inside the square root are the same.
If they are the same, just add the numbers in front of the radical. If they are not the same, the answer is just the problem stated.
Since they are the same, just add the numbers in front of the radical: 
which is 
Therefore, our final answer is the sum of the integers and the radical:
When adding and subtracting radicals, make the sure radicand or inside the square root are the same.
If they are the same, just add the numbers in front of the radical. If they are not the same, the answer is just the problem stated.
Since they are the same, just add the numbers in front of the radical:
Therefore, our final answer is the sum of the integers and the radical:
Solve.
Solve.
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When adding and subtracting radicals, make the sure radicand or inside the square root are the same. If they are the same, just add the numbers in front of the radical. If they are not the same, the answer is just the problem stated.
Even though it's not the same, double check you can simplify the radicand. Look for perfect squares.
Since 
, 
and 
and 
are perfect squares, we can rewrite like this:
and 
.
Now that we have the same radicand, we can add them easily to get:
.
When adding and subtracting radicals, make the sure radicand or inside the square root are the same. If they are the same, just add the numbers in front of the radical. If they are not the same, the answer is just the problem stated.
Even though it's not the same, double check you can simplify the radicand. Look for perfect squares.
Since
Now that we have the same radicand, we can add them easily to get:
Solve.
Solve.
Tap to see back →
When adding and subtracting radicals, make the sure radicand or inside the square root are the same.
If they are the same, just add the numbers in front of the radical.
If they are not the same, the answer is just the problem stated.
Since they are the same, just subtract the numbers in front: 
which is 
Therefore, our final answer is this sum with the radical added to the end:
When adding and subtracting radicals, make the sure radicand or inside the square root are the same.
If they are the same, just add the numbers in front of the radical.
If they are not the same, the answer is just the problem stated.
Since they are the same, just subtract the numbers in front:
Therefore, our final answer is this sum with the radical added to the end:
Solve.
Solve.
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When adding and subtracting radicals, make the sure radicand or inside the square root are the same.
If they are the same, just add the numbers in front of the radical.
If they are not the same, the answer is just the problem stated.
Since they are the same, just add and subtract the numbers in front: 
which is 
Therefore, the final answer will be this sum and the radical added to the end:
When adding and subtracting radicals, make the sure radicand or inside the square root are the same.
If they are the same, just add the numbers in front of the radical.
If they are not the same, the answer is just the problem stated.
Since they are the same, just add and subtract the numbers in front:
Therefore, the final answer will be this sum and the radical added to the end:
Solve.
Solve.
Tap to see back →
When adding and subtracting radicals, make the sure radicand or inside the square root are the same.
If they are the same, just add the numbers in front of the radical.
If they are not the same, the answer is just the problem stated.
Even though it's not the same, double check you can simplify the radicand. Look for perfect squares. Since 
and 
is a perfect square, we can rewrite like this: 
.
Now we have the same radicand, we can now add them easily to get 
.
When adding and subtracting radicals, make the sure radicand or inside the square root are the same.
If they are the same, just add the numbers in front of the radical.
If they are not the same, the answer is just the problem stated.
Even though it's not the same, double check you can simplify the radicand. Look for perfect squares. Since
Now we have the same radicand, we can now add them easily to get
Solve.
Solve.
Tap to see back →
When adding and subtracting radicals, make the sure radicand or inside the square root are the same. If they are the same, just add the numbers in front of the radical. If they are not the same, the answer is just the problem stated.
Even though it's not the same, double check you can simplify the radicand. Look for perfect squares.
Since 
and 
is a perfect square, we can rewrite like this: 
.
Now we have the same radicand, we can now subtract them easily to get 
.
When adding and subtracting radicals, make the sure radicand or inside the square root are the same. If they are the same, just add the numbers in front of the radical. If they are not the same, the answer is just the problem stated.
Even though it's not the same, double check you can simplify the radicand. Look for perfect squares.
Since
Now we have the same radicand, we can now subtract them easily to get
Solve.
Solve.
Tap to see back →
When adding and subtracting radicals, make the sure radicand or inside the square root are the same. If they are the same, just add the numbers in front of the radical. If they are not the same, the answer is just the problem stated.
Even though it's not the same, double check you can simplify the radicand. Look for perfect squares. 
and 
are perfect squares so we can rewrite like this:
Since 
and 
is a perfect square, we can rewrite like this:
.
Lets add everything up.
.
The reason this is the answer, because the 
is associated with the radical and we can't subtract a whole number with the radical. They are not the same.
When adding and subtracting radicals, make the sure radicand or inside the square root are the same. If they are the same, just add the numbers in front of the radical. If they are not the same, the answer is just the problem stated.
Even though it's not the same, double check you can simplify the radicand. Look for perfect squares.
Since
Lets add everything up.
The reason this is the answer, because the
Solve.
Solve.
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When adding and subtracting radicals, make the sure radicand or inside the square root are the same. If they are the same, just add the numbers in front of the radical. If they are not the same, the answer is just the problem stated. Even though it's not the same, double check you can simplify the radicand. Look for perfect squares.
Since
and 
are perfect squares, we can rewrite like this:
Lets add everything up.
When adding and subtracting radicals, make the sure radicand or inside the square root are the same. If they are the same, just add the numbers in front of the radical. If they are not the same, the answer is just the problem stated. Even though it's not the same, double check you can simplify the radicand. Look for perfect squares.
Since
Lets add everything up.