# SAT Math : How to simplify square roots

## Example Questions

### Example Question #53 : Basic Squaring / Square Roots

Simplify the following:

Explanation:

To solve, you must first break up 54 into its smallest prime factors. Those are:

Since our root has index 2, that means that for every 2 identical factors inside, you can pull 1 out. Thus, we get

### Example Question #54 : Basic Squaring / Square Roots

Simplify

Explanation:

To simplify a square root, we need to find perfect squares. In this case, it is .

### Example Question #55 : Basic Squaring / Square Roots

Simplify:

Explanation:

To simplify a square root, we need to find perfect squares. In this case, it is .

### Example Question #56 : Basic Squaring / Square Roots

Simplify:

Explanation:

To simplify a square root, we need to find perfect squares. In this case, it is . Since there is a number outside the radical, we ignore that for now and later we multiply the number and square root.

### Example Question #57 : Basic Squaring / Square Roots

Simplify:

Explanation:

To simplify a square root, we need to find perfect squares. In this case, it is . Since there is a number outside the radical, we ignore that for now and later we multiply the number and square root.

### Example Question #58 : Basic Squaring / Square Roots

Simplify:

Explanation:

To simplify radicals, we need to find a perfect square to factor out. In this case, its .

### Example Question #59 : Basic Squaring / Square Roots

Simplify:

Explanation:

To simplify radicals, we need to find a perfect square to factor out. In this case, its .

### Example Question #60 : Basic Squaring / Square Roots

Simplify:

Explanation:

To solve this, we know perfect squares are able to simplify easily to the base it is. Let's find all the perfect squares in .

### Example Question #61 : Basic Squaring / Square Roots

Simplify:

It's impossible because the value is negative.

Explanation:

Although the exponent is negative, we know that . Therefore, we have . Let's simplify this by finding perfect squares.

Simplify: