Question

What is the solution to the equation `1/(sqrt8)=4(m+2)`?

Answer 1

`m=1/(8sqrt2)-2`

Explanation:

Solve:

`1/sqrt8=4(m+2)`

Prime factorize `8`.

`1/sqrt(2^2xx2)=4(m+2)`

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

`1/(2sqrt2)=4(m+2)`

Divide both sides by `4`.

`1/(2sqrt2)-:4=m+2`

Apply rule: `a/b-:c/d=a/bxxd/c`

`1/(2sqrt2)xx1/4=m+2`

Simplify `1/(4xx2sqrt2)` to `1/(8sqrt2)`.

`1/(8sqrt2)=m+2`

Subtract `2` from both sides.

`1/(8sqrt2)-2=m`

Switch sides.

`m=1/(8sqrt2)-2`