Question from http://www.sgforums.com/forums/2297/topics/344321
A rectangular block has a square base. The length of each side of the base is (√5 - √3) m and the volume of the block is ( 4√3 - 2√5). Find , without using a calculator, the height of the block in the form of a√3 + b√5.
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Answer:
Volume of rectangular block = length * length * height
4√3 - 2√5 = (√5 - √3) * (√5 - √3) * height
4√3 - 2√5 = (5 - 2√15 + 3) * height
4√3 - 2√5 = (8 - 2√15) * height
Thus,
height = (4√3 - 2√5) / (8 - 2√15)
height = (2√3 - √5) / (4 - √15) =====> divide by 2 top and bottom. Easier to work with smaller numbers
height = {(2√3 - √5)(4 + √15)} / {(4 - √15)(4 + √15)} ===> Rationalisation
height = (8√3 - 4√5 + 6√5 - 5√3) / (16 - 15)
height = 3√3 + 2√5 (ans)
