GCSE Maths question?

Question

Hence Write √600 + √54/√338 in the form √q

You may use 338 = 2 x 13^2

Thanks.

Answer 1

Break the whole thing down:
√600 = √(100 * 6) = 10√3√2
√54/√338 = 3√3 √2 * 13√2 = 13 * 3 * 2√3 = 78√3
So the common factor is √3

√3[10√2 + 78]

Answer 2

sqr(100 x 6) + sqr (54 / 338 )
=10 sqr(6) + sqr(27/169)
=10 sqr(6) + 3 sqr(3) / 13