# PSAT Math : Square Roots and Operations

## Example Questions

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### Example Question #1 : Square Roots And Operations

Divide and simplify. Assume all integers are positive real numbers.

Explanation:

There are two ways to solve this problem. First you can divide the numbers under the radical. Then simplify.

Example 1

Example 2

Find the square root of both numerator and denominator, simplifying as much as possible then dividing out like terms.

Both methods will give you the correct answer of .

### Example Question #1 : Basic Squaring / Square Roots

(√27 + √12) / √3 is equal to

5/√3

(6√3)/√3

18

5

√3

5

Explanation:

√27 is the same as 3√3, while √12 is the same as 2√3.

3√3 + 2√3 = 5√3

(5√3)/(√3) = 5

### Example Question #3 : Square Roots And Operations

Simplify:

Explanation:

To simplfy, we must first distribute the square root.

Next, we can simplify each of the square roots.

### Example Question #4 : Square Roots And Operations

Find the quotient:

Explanation:

Find the quotient:

There are two ways to approach this problem.

Option 1: Combine the radicals first, the reduce

Option 2: Simplify the radicals first, then reduce

### Example Question #1 : Basic Squaring / Square Roots

Find the quotient:

Explanation:

Rationalize the denominator:

### Example Question #6 : Square Roots And Operations

Evaluate:

Explanation:

Let us factor 108 and 81

### Example Question #1 : Square Roots And Operations

Explanation:

Step one: Find the greatest square factor of each radical

For  this is , and for  it is .

Therefore:

### Example Question #1 : Basic Squaring / Square Roots

Simplify.

Explanation:

First step is to find perfect squares in all of our radicans.

After doing so you are left with

*Just like fractions you can only add together coefficents with like terms under the radical. *

### Example Question #2 : Basic Squaring / Square Roots

If  what is ?

Explanation:

Square both sides:

x = (32)2 = 92 = 81

Simplify: