How do you simplify $\sqrt{\frac{1}{8}}$ $sqrt(1/8)$ ?

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How do you simplify $\sqrt{\frac{1}{8}}$ $sqrt(1/8)$ ?

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Answer 1 · 2018-03-28T22:07:41

$\frac{\sqrt{2}}{4}$ $sqrt2/4$

Explanation:

Looking at the given expression:
$\sqrt{\frac{1}{8}}$ $sqrt(1/8)$

By: $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ $sqrt(a/b)= sqrta/sqrtb$

$\sqrt{\frac{1}{8}} = \frac{\sqrt{1}}{\sqrt{8}}$ $sqrt(1/8)=sqrt1/sqrt8$

Which is:

$\frac{\sqrt{1}}{\sqrt{8}} = \frac{1}{\sqrt{8}}$ $sqrt1/sqrt8= 1/sqrt8$

Simplify:
$\frac{1}{\sqrt{8}} = \frac{1}{\sqrt{2 \cdot 4}}$ $1/sqrt8=1/sqrt(2*4)$

$\frac{1}{\sqrt{2 \cdot 4}} = \frac{1}{2 \sqrt{2}}$ $1/sqrt(2*4)= 1/(2sqrt2)$

Rationalize the denominator:
$\frac{1}{2 \sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{4}$ $1/(2sqrt2)*sqrt2/sqrt2= sqrt2/4$

Answer 2 · 2018-03-28T22:08:30

$\sqrt{\frac{1}{8}} = \frac{\sqrt{2}}{4}$ $sqrt(1/8)=color(blue)(sqrt2/4$

Explanation:

Simplify:

$\sqrt{\frac{1}{8}}$ $sqrt(1/8)$

Apply square root rule: $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}; b \neq 0$ $sqrt(a/b)=sqrta/sqrtb; b!=0$

$\frac{\sqrt{1}}{\sqrt{8}}$ $sqrt1/sqrt8$

Simplify $\sqrt{1}$ $sqrt1$ to $1$ $1$ .

$\frac{1}{\sqrt{8}}$ $1/sqrt8$

Rationalize the denominator.

$\frac{1}{\sqrt{8}} \times \frac{\sqrt{8}}{\sqrt{8}}$ $1/sqrt8xxsqrt8/sqrt8$

$\frac{\sqrt{8}}{\sqrt{8} \sqrt{8}}$ $sqrt8/(sqrt8sqrt8)$

Apply square root rule: $\sqrt{a} \sqrt{a} = a$ $sqrtasqrta=a$

$\frac{\sqrt{8}}{8}$ $sqrt8/8$

Prime factorize $\sqrt{8}$ $sqrt8$ .

$\frac{\sqrt{2 \times 2 \times 2}}{8} =$ $sqrt(2xx2xx2)/8=$

$\frac{\sqrt{2^{2} \times 2}}{8}$ $sqrt(2^2xx2)/8$

Apply square root rule: $\sqrt{a^{2}} = a$ $sqrt(a^2)=a$

$(color(red)cancel(color(black)(2))^1sqrt2)/color(red)cancel(color(black)(8))^4$

Simplify.

$sqrt2/4$

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