SAT Math : How to find the common factors of squares
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Example Question #2 : Factoring And Simplifying Square Roots
If m and n are postive integers and 4m = 2n, what is the value of m/n?
16
4
1/2
2
8
1/2
- 22 = 4. Also, following the rules of exponents, 41 = 1.
- One can therefore say that m = 1 and n = 2.
- The question asks to solve for m/n. Since m = 1 and n = 2, m/n = 1/2.
Example Question #3 : Arithmetic
Simplify:
When simplifying the square root of a number that may not have a whole number root, it's helpful to approach the problem by finding common factors of the number inside the radicand. In this case, the number is 24,300.
What are the factors of 24,300?
24,300 can be factored into:
When there are factors that appear twice, they may be pulled out of the radicand. For instance, 100 is a multiple of 24,300. When 100 is further factored, it is 
But 243 can also be factored:
Following the same principle as for the 100, the problem would become
9 and 10 may be multiplied together, yielding the final simplified answer of
Example Question #1 : Simplifying Square Roots
To solve the equation 
When a factor appears twice, we can take it out of the square root.
Now the numbers can be added directly because the expressions under the square roots match.
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