SAT Math : How to simplify square roots

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #121 : Arithmetic

Simplify the following:

Possible Answers:

Correct answer:

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 #21 : How To Simplify Square Roots

Simplify 

Possible Answers:

Correct answer:

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: 

Possible Answers:

Correct answer:

Explanation:

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

Example Question #21 : How To Simplify Square Roots

Simplify: 

Possible Answers:

Correct answer:

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 #51 : Basic Squaring / Square Roots

Simplify: 

Possible Answers:

Correct answer:

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 #21 : How To Simplify Square Roots

Simplify: 

Possible Answers:

Correct answer:

Explanation:

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

Example Question #121 : Arithmetic

Simplify: 

Possible Answers:

Correct answer:

Explanation:

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

Example Question #22 : How To Simplify Square Roots

Simplify: 

Possible Answers:

Correct answer:

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: 

Possible Answers:

It's impossible because the value is negative.

Correct answer:

Explanation:

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

Example Question #61 : Basic Squaring / Square Roots

Simplify: 

Possible Answers:

Correct answer:

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 .

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