1.2: Simplifying surds and solving with fractional indices

0606/11/M/J/17 — Question 3 · 6 marks

(a)

Simplify

\sqrt{x^{8}y^{10}} \div \sqrt[3]{x^{3}y^{-6}}

, giving your answer in the form

x^{a}y^{b}

, where

a

and

b

are integers.

[2]

(b)(i)

Show that

4(t-2)^{\frac{1}{2}} + 5(t-2)^{\frac{3}{2}}

can be written in the form

(t-2)^{p}(qt + r)

, where

p

q

and

r

are constants to be found.

[3]

(b)(ii)

Hence solve the equation

4(t-2)^{\frac{1}{2}} + 5(t-2)^{\frac{3}{2}} = 0

[1]