How do you simplify #sqrt(300x^2)#?

1 Answer
Aug 28, 2016

Answer:

For any Real value of #x#

#sqrt(300x^2) = 10sqrt(3)abs(x)#

If we know that #x >= 0# then this simplifies further to:

#10sqrt(3)x#

Explanation:

Note that for any non-zero value of #x#, #x^2# has two square roots, namely #x# and #-x#.

The expression #sqrt(x^2)# denotes the principal square root, which is the non-negative one.

Hence: #sqrt(x^2) = abs(x)#

So we find:

#sqrt(300x^2) = sqrt(10^2*3*x^2) = sqrt(10^2)*sqrt(3)*sqrt(x^2) = 10sqrt(3)abs(x)#

If we know that #x >= 0# then #abs(x) = x# and this simplifies further to #10sqrt(3)x#