How do you simplify #sqrt(28a^2b^3)#?

Question

1708 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-17T17:50:28

#2sqrt7ab^(3/2)#

The easiest way to simplify this surd is to separate it into its constituent surds, that is, the surds that make it up:

#sqrt(ab) = sqrtaxxsqrtb#

So if we apply the same rule to #sqrt(28a^2b^3)# we get:

#sqrt(28a^2b^3) = sqrt28xxsqrt(a^2)xxsqrt(b^3#

We can do this again with each of these surds to simplify it again:

#sqrt28xxsqrt(a^2)xxsqrt(b^3) =sqrt4xxsqrt7xxsqrtaxxsqrtaxxsqrtbxxsqrtbxxsqrtb#

We can evaluate these surds by separating them into like factors:

#sqrt4xxsqrt7=2xxsqrt7=2sqrt7#
#sqrtaxxsqrta=a#
#sqrtbxxsqrtbxxsqrtb=bsqrtb=b^(3/2)#

Now we need to multiply each of these factors:

#2sqrt7ab^(3/2)#