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SAT Math : How to find the square root of a decimal

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #31 : Decimals

Evaluate: $\sqrt{1.44}$

Possible Answers:

$\pm0.012$

0.0012

$\pm1.2$

$\pm0.12$

1.2

Correct answer:

$\pm1.2$

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.

$\sqrt{1.44}= \pm1.2$

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Example Question #11 : Basic Squaring / Square Roots

Without using a calculator, solve for x:

x^2 = 0.16

Possible Answers:

$\pm0.4$

$\pm0.8$

$\pm0.9$

$\pm0.5$

$\pm\frac{2}{\sqrt{10}}$

Correct answer:

$\pm0.4$

Explanation:

Simplifying the given equation gives us

$x=\pm\sqrt{\frac{16}{100}}=\pm\frac{\sqrt{16}}{\sqrt{100}}$

$=\pm\frac{4}{10}=\pm0.4$

Therefore, the correct answer is $\pm0.4$ .

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Example Question #383 : Arithmetic

If x^2=0.000004 and x>0 , what is the value of ?

Possible Answers:

0.002

0.02

0.2

0.0002

Correct answer:

0.002

Explanation:

We are given the equation x^2=0.000004 . To determine the value of , take the square root of both sides.

$x=\sqrt{0.000004}$ .

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

$\sqrt{4}=\pm2$

$\sqrt{0.04}=\pm0.2$

$\sqrt{0.0004}=\pm0.02$

Each succeeding radicand is $\frac{1}{100}$ of the previous radicand, and the value of each succeeding square root is $\frac{1}{10}$ of the previous value. Continuing the pattern:

$\sqrt{0.000004}=\pm0.002$ . However, we are also given the condition that x>0 ; hence, we eliminate the extraneous solution x=-0.002 and conclude that the only valid solution of x^2=0.000004 is x=0.002 .

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SAT Math : How to find the square root of a decimal

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #31 : Decimals

Example Question #11 : Basic Squaring / Square Roots

Example Question #383 : Arithmetic

All SAT Math Resources

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DMCA Complaint

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