### 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 #1 : Basic Squaring / Square Roots

(√27 + √12) / √3 is equal to

**Possible Answers:**

5/√3

(6√3)/√3

18

5

√3

**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 #1 : Basic Squaring / Square Roots

Find the quotient:

**Possible Answers:**

**Correct answer:**

Simplify each radical:

Rationalize the denominator:

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

Evaluate:

**Possible Answers:**

None of the available answers

**Correct answer:**

Let us factor 108 and 81

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

**Possible Answers:**

**Correct answer:**

Step one: Find the greatest square factor of each radical

For this is , and for it is .

Therefore:

Step two: Simplify the radicals

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

Simplify.

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

Square both sides:

x = (3^{2})^{2}^{ }= 9^{2} = 81

### Example Question #10 : Square Roots And Operations

Simplify:

**Possible Answers:**

**Correct answer:**

To combine radicals, they must have the same radicand. Therefore, we must find the perfect squares in each of our square roots and pull them out.

Now, we plug these equivalent expressions back into our equation and simplify:

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