AM-1439

Surds and rationalising

A Math · Secondary 4 · Hard · Surds and rationalising

A rectangular tank has a base area of

(9 + 4\sqrt{3})\text{ cm}^2

and a volume of

(30 + 22\sqrt{3})\text{ cm}^3

. Find, without using a calculator, the height of the tank in cm, in the form

(a + b\sqrt{3})

, where

a

and

b

are integers.

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