Please solve this? question in the attachment

enter image source here

2 Answers
May 10, 2018

=203/9sqrt3

Explanation:

We will use the fact that sqrt(a/b)=sqrta/sqrtb

7*sqrt1/sqrt3-7/3*sqrt1/sqrt3+3sqrt147

=7/sqrt3-7/(3sqrt3)+3sqrt147

=(7sqrt3)/3-(7sqrt3)/9+3sqrt147

=(21sqrt3)/9-(7sqrt3)/9+3sqrt147

=(14sqrt3)/9+3sqrt147

I've left the 3sqrt147 up till now, cos its nasty to deal with. However, seeing that we have an expression with sqrt3, there's a good chance that 147 will be equal to three times a square number. Some good ol' bus shelter long division (or using a calculator if you're allowed) will show you that 147=3xx49 Since 49 is a square number, we can work on simplifying this more

=(14sqrt3)/9+3[sqrt(3xx49)]

=(14sqrt3)/9+3(7sqrt3)

=(14sqrt3)/9+21sqrt3

=(14sqrt3)/9+(189sqrt3)/9

=203/9sqrt3

May 10, 2018

=39.06736822

Explanation:

sqrt(1/3) =sqrt3/3

sqrt(147)=sqrt49 xx sqrt3=7sqrt3

7sqrt(1/3)-2 1/3sqrt(1/3)+3sqrt(147)

=(7sqrt3)/3-(7sqrt3)/9+21sqrt3

(14sqrt3)/9+21sqrt3=(203sqrt3)/9

=39.06736822