Question

How do you solve `81m^2=64`?

Answer 1

`m=-8/9 or m=+8/9`

Explanation:

Since `81m^2=(9m)^2`
`81m^2=64`
`rarrcolor(white)("XXX")(9m)^2=64`
then taking the square root of both sides
`rarrcolor(white)("XXX")9m=+-8`
or
`color(white)("XXXXX")m=+-8/9`

Answer 2

`m=+-8/9`

Explanation:

Given:`" "81m^2=64`

Divide both sides by 81

`81/81xxm^2=64/81`

But `81/81=1`

`m^2=64/81`

Square root both sides

`m=+-sqrt(64/81)`

`m=+-sqrt(64)/sqrt(81)`

`m=+-8/9`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Why is this `+-`?

Consider the example: `(+2)xx(+2)=(-2)xx(-2)= +4`

If the signs are the same in multiply or divide then the answer is positive.

So `m^2=(-8/9)^2=(+8/9)^2`

So `m=+-8/9`