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

1 Answer
Apr 29, 2016

Answer:

#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)#