### All PSAT Math Resources

## Example Questions

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

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

**Possible Answers:**

**Correct answer:**

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 #2 : Square Roots And Operations

(√27 + √12) / √3 is equal to

**Possible Answers:**

(6√3)/√3

√3

5

5/√3

18

**Correct answer:**

5

√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:

**Possible Answers:**

**Correct answer:**

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:

**Possible Answers:**

**Correct answer:**

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 #5 : Square Roots And Operations

Find the quotient:

**Possible Answers:**

**Correct answer:**

Simplify each radical:

Rationalize the denominator: