Question

How do you simplify `sqrt(9x^4)`?

Answer 1

`3x^2`

Explanation:

`9=3^2" and "x^4 = (x^2)^2`

Multiply any number by 1 and you do not change that number's value. I am including the value 1 just to demonstrate a process.

So write as:`" sqrt(1xx3^2xx(x^2)^2)`

Taking all squared values outside the square root removing the square. For `(x^2)^2` you remove the outer square.

`3xx x^2xxsqrt(1)`

But `sqrt(1) = 1` so we have

`3xx x^2xx1" "=" "3x^2`
'~~~~~~~~~~~~~~~~~~~~~~~~~~
This trick of multiply by 1 is used in higher maths when you have
`sqrt(-4)->sqrt(-1xx4)->2sqrt(-1)`