Question

How do you simplify `sqrt(10a) * sqrt(30a)` ?

Answer 1

`10asqrt(3)`

Explanation:

`sqrt(10a)*sqrt(30a)`

Know that, `sqrt(a)*sqrt(b)=sqrt(ab)` for `a, b>0`

`:.=sqrt(10a*30a)`

`=sqrt(300a^2)`

`=asqrt(300)`

`=asqrt(100*3)`

`=10asqrt(3)`

Answer 2

`sqrt(10a) * sqrt(30a) = 10sqrt(3)a`

Explanation:

If `a >= 0` and `b` is any number (positive, zero, negative or complex) then:

`sqrt(ab) = sqrt(a)sqrt(b)`

Moreover, if `a` is any number, then `sqrt(a)` is by definition a value satisfying:

`(sqrt(a))^2 = a`

So we find:

`sqrt(10a) * sqrt(30a) = sqrt(10) * sqrt(a) * sqrt(30) * sqrt(a)`

`color(white)(sqrt(10a) * sqrt(30a)) = sqrt(10) * sqrt(a) * sqrt(10) * sqrt(3) * sqrt(a)`

`color(white)(sqrt(10a) * sqrt(30a)) = (sqrt(10))^2 * sqrt(3) * (sqrt(a))^2`

`color(white)(sqrt(10a) * sqrt(30a)) = 10sqrt(3)a`