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Example Questions
Example Question #1 : Square Roots And Operations
Find the product:
Simplify the radicals, then multiply:
Example Question #1 : Square Roots And Operations
Simplify the following completely:
To simplify this expression, simply multiply the radicands and reduce to simplest form.
Example Question #3 : How To Multiply Square Roots
Simplify:
When multiplying square roots, the easiest thing to do is first to factor each root. Thus:
Now, when you combine the multiplied roots, it will be easier to come to your final solution. Just multiply together everything "under" the roots:
Finally this can be simplified as:
Example Question #4 : How To Multiply Square Roots
Simplify the following:
When multiplying square roots, the easiest thing to do is first to factor each root. Thus:
Now, when you combine the multiplied roots, it will be easier to come to your final solution. Remember that multiplying roots is very easy! Just multiply together everything "under" the roots:
Finally this can be simplified as:
Example Question #5 : How To Multiply Square Roots
State the product:
Don't try to do too much at first for this problem. Multiply your radicals and your coefficients, then worry about any additional simplification.
Now simplify the radical.
Example Question #6 : How To Multiply Square Roots
Find the product:
Don't try to do too much at first for this problem. Multiply your radicals and your coefficients, then worry about any additional simplification.
Now, simplify your radical.
Example Question #1 : Square Roots And Operations
x4 = 100
If x is placed on a number line, what two integers is it between?
3 and 4
5 and 6
Cannot be determined
2 and 3
4 and 5
3 and 4
It might be a little difficult taking a fourth root of 100 to isolate x by itself; it might be easier to select an integer and take that number to the fourth power. For example 34 = 81 and 44 = 256. Since 34 is less than 100 and 44 is greater than 100, x would lie between 3 and 4.
Example Question #1 : How To Find A Ratio Of Square Roots
What is the ratio of to
?
The ratio of two numbers is merely the division of the two values. Therefore, for the information given, we know that the ratio of
to
can be rewritten:
Now, we know that the square root in the denominator can be "distributed" to the numerator and denominator of that fraction:
Thus, we have:
To divide fractions, you multiply by the reciprocal:
Now, since there is one in
, you can rewrite the numerator:
This gives you:
Rationalize the denominator by multiplying both numerator and denominator by :
Let's be careful how we write the numerator so as to make explicit the shared factors:
Now, reduce:
This is the same as
Example Question #1 : How To Find A Ratio Of Square Roots
and
What is the ratio of to
?
To find a ratio like this, you need to divide by
. Recall that when you have the square root of a fraction, you can "distribute" the square root to the numerator and the denominator. This lets you rewrite
as:
Next, you can write the ratio of the two variables as:
Now, when you divide by a fraction, you can rewrite it as the multiplication by the reciprocal. This gives you:
Simplifying, you get:
You should rationalize the denominator:
This is the same as:
Example Question #41 : Arithmetic
Find the sum:
Find the Sum:
Simplify the radicals:
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