GRE Math : Arithmetic
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Example Questions
Example Question #1 : How To Find The Common Factors Of Squares
Reduce.
To simplify, we must try to find factors which are perfect squares. In this case 36 is a factor of 72 and is also a perfect square.
To reduce this expression, use the following arithmetic steps:
Example Question #1 : Simplifying Square Roots
Which quantity is greater: 
Not enough information to determine the relationship between these two quantities.
To simplify, we must try to find factors which are perfect squares. In this case 30 is a factor of 900 and is also a perfect square.
The square root of 
However,
Thus, 
Example Question #3 : How To Find The Common Factors Of Squares
Reduce.
To simplify, we must try to find factors which are perfect squares. In this case 16 is a factor of 32 and is also a perfect square.
To reduce this expression, use the following steps:
Example Question #11 : How To Find The Common Factors Of Squares
Find the square root of 
To simplify, we must try to find factors which are perfect squares. In this case 4 is a factor of 164 and is also a perfect square.
To find the square root of 
Example Question #12 : Arithmetic
Reduce.
Use the following arithmetic steps to reduce 
To simplify, we must try to find factors which are perfect squares. In this case 64 is a factor of 192 and is also a perfect square.
Note 
Example Question #11 : Arithmetic
Reduce.
To reduce this expression, first find factors of 
To simplify, we must try to find factors which are perfect squares. In this case 16 is a factor of 368 and is also a perfect square.
The solution is:
Example Question #11 : Arithmetic
Find the square root of 
To reduce this expression, first find factors of 
To simplify, we must try to find factors which are perfect squares. In this case 16 is a factor of 416 and is also a perfect square.
The solution is:
Example Question #1 : How To Simplify Square Roots
Simplify the following: (√(6) + √(3)) / √(3)
None of the other answers
3√(2)
√(2) + 1
√(3)
1
√(2) + 1
Begin by multiplying top and bottom by √(3):
(√(18) + √(9)) / 3
Note the following:
√(9) = 3
√(18) = √(9 * 2) = √(9) * √(2) = 3 * √(2)
Therefore, the numerator is: 3 * √(2) + 3. Factor out the common 3: 3 * (√(2) + 1)
Rewrite the whole fraction:
(3 * (√(2) + 1)) / 3
Simplfy by dividing cancelling the 3 common to numerator and denominator: √(2) + 1
Example Question #11 : Simplifying Square Roots
what is
√0.0000490
0.00007
0.07
0.007
49
7
0.007
easiest way to simplify: turn into scientific notation
√0.0000490= √4.9 X 10-5
finding the square root of an even exponent is easy, and 49 is a perfect square, so we can write out an improper scientific notation:
√4.9 X 10-5 = √49 X 10-6
√49 = 7; √10-6 = 10-3 this is equivalent to raising 10-6 to the 1/2 power, in which case all that needs to be done is multiply the two exponents: 7 X 10-3= 0.007
Example Question #1 : How To Simplify Square Roots
Simplify:
In order to take the square root, divide 576 by 2.
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