Question

How do you simplify `sqrt(1/8)`?

Answer 1

`sqrt2/4`

Explanation:

Looking at the given expression:
`sqrt(1/8)`

By: `sqrt(a/b)= sqrta/sqrtb`

`sqrt(1/8)=sqrt1/sqrt8`

Which is:

`sqrt1/sqrt8= 1/sqrt8`

Simplify:
`1/sqrt8=1/sqrt(2*4)`

`1/sqrt(2*4)= 1/(2sqrt2)`

Rationalize the denominator:
`1/(2sqrt2)*sqrt2/sqrt2= sqrt2/4`

Answer 2

`sqrt(1/8)=color(blue)(sqrt2/4`

Explanation:

Simplify:

`sqrt(1/8)`

Apply square root rule: `sqrt(a/b)=sqrta/sqrtb; b!=0`

`sqrt1/sqrt8`

Simplify `sqrt1` to `1`.

`1/sqrt8`

Rationalize the denominator.

`1/sqrt8xxsqrt8/sqrt8`

`sqrt8/(sqrt8sqrt8)`

Apply square root rule: `sqrtasqrta=a`

`sqrt8/8`

Prime factorize `sqrt8`.

`sqrt(2xx2xx2)/8=`

`sqrt(2^2xx2)/8`

Apply square root rule: `sqrt(a^2)=a`

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

Simplify.

`sqrt2/4`