Question

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

Answer 1

Both the numerator and denominator of a fraction can be multiplied by the same real number (not equal to zero), without changing the value of a fraction.

For instance, `3/4=(3*6)/(4*6)=(3*0.123456)/(4*0.123456)`

Let's use this rule and multiply the numerator and the denominator of our fraction by `sqrt(8)`:

`8/sqrt(8)=(8*sqrt(8))/(sqrt(8)*sqrt(8))=(8*sqrt(8))/8`

Additionally, both the numerator and denominator of a fraction can be divided by the same real number (not equal to zero), without changing the value of a fraction.

Let's divide both the numerator and the denominator of our fraction by `8`:

`(8*sqrt(8))/8=sqrt(8)/1=sqrt(8)`

`:., 8/sqrt(8)=sqrt(8)`

Answer 2

`8/sqrt8 = (sqrt8)^2/sqrt8 = sqrt8 = sqrt(4*2) = 2 sqrt2`