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Question
Simplify the following using multiplication and division properties of surds:
`[sqrt(225/729) - sqrt(25/144)] ÷ sqrt(16/81)`
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Solution
`[sqrt(225/729) - sqrt(25/144)] ÷ sqrt(16/81)`
= `[ sqrt((3^2 xx 5^2)/(3^2 xx 3^2 xx 3^2)) - sqrt((5^2)/(2^2 xx 2^2 xx 3^2))] ÷ sqrt(2^4/3^4)`
= `[(3 xx 5)/(3 xx 3 xx 3) - 5/(2 xx 2 xx 3)] ÷ 2^2/3^2`
= `[5/9 - 5/12] ÷ 4/9`
= `((20 - 15)/36) ÷ 4/9`
= `5/36 xx 9/4`
= `(5 xx 1)/(4 xx 4)`
= `5/16`
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