SAT Math : How to add square roots

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1 : How To Add Square Roots

If \sqrt{x}=3^2 what is x?

Possible Answers:

9

27

3

729

81

Correct answer:

81

Explanation:

Square both sides:

x = (32)2 = 92 = 81

Example Question #15 : Square Roots And Operations

Simplify in radical form:

Possible Answers:

Correct answer:

Explanation:

To simplify, break down each square root into its component factors:

You can remove pairs of factors and bring them outside the square root sign. At this point, since each term shares , you can add them together to yield the final answer:

Example Question #2 : How To Add Square Roots

Simplify: 

 

Possible Answers:

None of the other answers

Correct answer:

Explanation:

Take each fraction separately first:

(2√3)/(√2) = [(2√3)/(√2)] * [(√2)/(√2)] = (2 * √3 * √2)/(√2 * √2) = (2 * √6)/2 = √6

Similarly:

(4√2)/(√3) = [(4√2)/(√3)] * [(√3)/(√3)] = (4√6)/3 = (4/3)√6

Now, add them together:

√6 + (4/3)√6 = (3/3)√6 + (4/3)√6 = (7/3)√6

Example Question #3 : How To Add Square Roots

Simplify the following expression: 

Possible Answers:

Correct answer:

Explanation:

Begin by factoring out each of the radicals:

For the first two radicals, you can factor out a  or :

The other root values cannot be simply broken down. Now, combine the factors with :

This is your simplest form.

Example Question #36 : Basic Squaring / Square Roots

Solve for .

Note, :

Possible Answers:

Correct answer:

Explanation:

Begin by getting your  terms onto the left side of the equation and your numeric values onto the right side of the equation:

Next, you can combine your radicals. You do this merely by subtracting their respective coefficients:

Now, square both sides:

Solve by dividing both sides by :

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