SAT Math : Basic Squaring / Square Roots

Study concepts, example questions & explanations for SAT Math

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Example Questions

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Example Question #11 : Basic Squaring / Square Roots

Solve for :

Possible Answers:

Correct answer:

Explanation:

Just like any other equation, isolate your variable. Start by multiplying both sides by :

Now, this is the same as:

You know that  is . You can intelligently rewrite this problem as:

, which is the same as:

Example Question #1 : How To Find The Square Root Of A Decimal

Find the square root of the following decimal:

Possible Answers:

Correct answer:

Explanation:

To find the square root of this decimal we convert it into scientific notation.

Because  has an even exponent, we can divide the exponenet by 2 to get its square root.  is a perfect square, whose square root is .

Example Question #11 : Basic Squaring / Square Roots

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

The square root of a number returns a positive and negative number that multiplies by itself to obtain the number inside the square root.

Example Question #32 : Decimals

Without using a calculator, solve for x:

Possible Answers:

Correct answer:

Explanation:

Simplifying the given equation gives us

Therefore, the correct answer is .

 

Example Question #33 : Decimals

If  and , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

We are given the equation . To determine the value of , take the square root of both sides.

.

To calculate this value, take note of the following pattern:

Each succeeding radicand is  of the previous radicand, and the value of each succeeding square root is   of the previous value. Continuing the pattern:

. However, we are also given the condition that ; hence, we eliminate the extraneous solution  and conclude that the only valid solution of  is .

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