### All SAT Math Resources

## Example Questions

### Example Question #1 : Factoring And Simplifying Square Roots

Simplify

9 ÷ √3

**Possible Answers:**

2

3√3

3

not possible

none of these

**Correct answer:**

3√3

in order to simplify a square root on the bottom, multiply top and bottom by the root

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

Simplify:

√112

**Possible Answers:**

4√10

12

10√12

20

4√7

**Correct answer:**

4√7

√112 = {√2 * √56} = {√2 * √2 * √28} = {2√28} = {2√4 * √7} = 4√7

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

Simplify:

√192

**Possible Answers:**

**Correct answer:**8√3

√192 = √2 X √96

√96 = √2 X √48

√48 = √4 X√12

√12 = √4 X √3

√192 = √(2X2X4X4) X √3

= √4X√4X√4 X √3

= 8√3

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

What is the simplest way to express ?

**Possible Answers:**

**Correct answer:**

First we will list the factors of 3888:

### Example Question #1 : Simplifying Square Roots

Simplify:

**Possible Answers:**

**Correct answer:**

4√27 + 16√75 +3√12 =

4*(√3)*(√9) + 16*(√3)*(√25) +3*(√3)*(√4) =

4*(√3)*(3) + 16*(√3)*(5) + 3*(√3)*(2) =

12√3 + 80√3 +6√3= 98√3

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

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

**Possible Answers:**

√(3)

1

√(2) + 1

3√(2)

None of the other answers

**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

0.07

49

7

0.00007

**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 #2 : How To Simplify Square Roots

Simplfy the following radical .

**Possible Answers:**

**Correct answer:**

You can rewrite the equation as .

This simplifies to .