PSAT Math : How to divide square roots
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Example Questions
Example Question #1 : Basic Squaring / Square Roots
Divide and simplify. Assume all integers are positive real numbers.
There are two ways to solve this problem. First you can divide the numbers under the radical. Then simplify.
Example 1
Example 2
Find the square root of both numerator and denominator, simplifying as much as possible then dividing out like terms.
Both methods will give you the correct answer of 
Example Question #1 : How To Divide Square Roots
(√27 + √12) / √3 is equal to
18
(6√3)/√3
5/√3
5
√3
5
√27 is the same as 3√3, while √12 is the same as 2√3.
3√3 + 2√3 = 5√3
(5√3)/(√3) = 5
Example Question #1 : Square Roots And Operations
Simplify:
To simplfy, we must first distribute the square root.
Next, we can simplify each of the square roots.
Example Question #3 : Basic Squaring / Square Roots
Find the quotient:
Find the quotient:
There are two ways to approach this problem.
Option 1: Combine the radicals first, the reduce
Option 2: Simplify the radicals first, then reduce
Example Question #1 : Square Roots And Operations
Find the quotient:
Simplify each radical:
Rationalize the denominator:
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