### All GRE Math Resources

## Example Questions

### Example Question #1 : How To Simplify Square Roots

Simplify the following: (√(6) + √(3)) / √(3)

**Possible Answers:**

None of the other answers

3√(2)

√(3)

√(2) + 1

1

**Correct answer:**

√(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 #1 : How To Simplify Square Roots

what is

√0.0000490

**Possible Answers:**

0.007

49

0.07

0.00007

7

**Correct answer:**

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:

**Possible Answers:**

**Correct answer:**

In order to take the square root, divide 576 by 2.

### Example Question #1 : How To Simplify Square Roots

Simplify .

**Possible Answers:**

**Correct answer:**

### Example Question #1 : How To Simplify Square Roots

Simplfy the following radical .

**Possible Answers:**

**Correct answer:**

You can rewrite the equation as .

This simplifies to .

### Example Question #1 : Simplifying Square Roots

Which of the following is equal to ?

**Possible Answers:**

**Correct answer:**

√75 can be broken down to √25 * √3. Which simplifies to 5√3.

### Example Question #1 : Simplifying Square Roots

Simplify .

**Possible Answers:**

**Correct answer:**

Rewrite what is under the radical in terms of perfect squares:

Therefore, .

### Example Question #21 : Arithmetic

What is ?

**Possible Answers:**

**Correct answer:**

We know that 25 is a factor of 50. The square root of 25 is 5. That leaves which can not be simplified further.

### Example Question #21 : Arithmetic

Which of the following is equivalent to ?

**Possible Answers:**

**Correct answer:**

Multiply by the conjugate and the use the formula for the difference of two squares:

### Example Question #2 : Simplifying Square Roots

Which of the following is the most simplified form of:

**Possible Answers:**

**Correct answer:**

First find all of the prime factors of

So