SAT Math : SAT Mathematics
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Example Questions
Example Question #1031 : Sat Mathematics
Simplify:
To simplify the radical, we need to find perfect squares. Then if possible, we can reduc the fraction.
Example Question #1032 : Sat Mathematics
Simplify:
To simplify the radical, let's deal with the parentheses first and apply the exponents. Reduce if necessary.
Example Question #1033 : Sat Mathematics
Simplify:
To eliminate a radical expression, we need to multiply top and bottom by the conjugate which is opposite the sign in the expression. Then simplify if necessary.
Example Question #82 : Basic Squaring / Square Roots
Simplify:
To simplify square roots, we need to find perfect squares to factor out.
We can also simplify
Thus,
We can compute the numbers outside to get a final answer of 
Example Question #1034 : Sat Mathematics
Simplify:
To eliminate a radical expression, we need to multiply top and bottom by the denominator.
Then simplify if necessary.
Example Question #82 : Basic Squaring / Square Roots
If 
In order to simplify the expression, we must see if we can factor out any perfect squares.
In this case, we can factor out 16x2.
Because of the rules of square roots, this can be rewritten as:
Because 
Thus, we can rewrite as
Example Question #51 : How To Simplify Square Roots
Simplify:
To simplify square roots, factor the inside completely to find perfect squares:
Then separate into several roots being multiplied:
Simplify:
Example Question #1 : How To Find The Common Factors Of Squares
If m and n are postive integers and 4m = 2n, what is the value of m/n?
1/2
4
16
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 #81 : 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 #2 : Arithmetic
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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