Pre-Algebra Examples

10 - 4 \sqrt{\frac{1}{16}}

$10 - 4 \sqrt{\frac{1}{16}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite

\sqrt{\frac{1}{16}}

$\sqrt{\frac{1}{16}}$ as

\frac{\sqrt{1}}{\sqrt{16}}

$\frac{\sqrt{1}}{\sqrt{16}}$ .

10 - 4 \frac{\sqrt{1}}{\sqrt{16}}

$10 - 4 \frac{\sqrt{1}}{\sqrt{16}}$

Step 1.2

Any root of

1

$1$ is

1

$1$ .

10 - 4 \frac{1}{\sqrt{16}}

$10 - 4 \frac{1}{\sqrt{16}}$

Step 1.3

Simplify the denominator.

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Step 1.3.1

Rewrite

16

$16$ as

4^{2}

$4^{2}$ .

10 - 4 \frac{1}{\sqrt{4^{2}}}

$10 - 4 \frac{1}{\sqrt{4^{2}}}$

Step 1.3.2

Pull terms out from under the radical, assuming positive real numbers.

10 - 4 (\frac{1}{4})

$10 - 4 (\frac{1}{4})$

10 - 4 (\frac{1}{4})

$10 - 4 (\frac{1}{4})$

Step 1.4

Cancel the common factor of

4

$4$ .

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Step 1.4.1

Factor

4

$4$ out of

- 4

$- 4$ .

10 + 4 (- 1) \frac{1}{4}

$10 + 4 (- 1) \frac{1}{4}$

Step 1.4.2

Cancel the common factor.

$10 + 4 \cdot - 1 \frac{1}{4}$

Step 1.4.3

Rewrite the expression.

$10 - 1$

Step 2

Subtract

$1$ from

$10$ .

$9$