All PSAT Math Resources
Example Questions
Example Question #1 : How To Divide 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
√3
(6√3)/√3
5
5/√3
18
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 #3 : Basic Squaring / Square Roots
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 #4 : Basic Squaring / Square Roots
Find the quotient:
Simplify each radical:
Rationalize the denominator:
Example Question #22 : Basic Squaring / Square Roots
Evaluate:
None of the available answers
Let us factor 108 and 81
Example Question #1 : How To Subtract Square Roots
Step one: Find the greatest square factor of each radical
For this is , and for it is .
Therefore:
Step two: Simplify the radicals
Example Question #1 : How To Add Square Roots
Simplify.
First step is to find perfect squares in all of our radicans.
After doing so you are left with
*Just like fractions you can only add together coefficents with like terms under the radical. *
Example Question #21 : Basic Squaring / Square Roots
If what is ?
Square both sides:
x = (32)2 = 92 = 81
Example Question #5 : Basic Squaring / Square Roots
Simplify:
To combine radicals, they must have the same radicand. Therefore, we must find the perfect squares in each of our square roots and pull them out.
Now, we plug these equivalent expressions back into our equation and simplify:
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