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Question
Rationalise the denominators of : `[ 2√5 + 3√2 ]/[ 2√5 - 3√2 ]`
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Solution
`[ 2√5 + 3√2 ]/[ 2√5 - 3√2 ] xx [ 2√5 + 3√2 ]/[ 2√5 + 3√2 ]`
= `[( 2sqrt5 + 3sqrt2)^2]/[ (2sqrt5)^2 - (3sqrt2)^2]`
= `[ 4 xx 5 + 9 xx 2 + 12sqrt10 ]/[ 20 -18 ]`
= `[ 20 + 18 + 12sqrt10 ]/2`
= `[ 38 + 12sqrt10 ]/2`
= `[2( 19 + 6sqrt10 )]/2`
= 19 + 6√10
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