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प्रश्न
Rationales the denominator and simplify:
`(5 + 2sqrt3)/(7 + 4sqrt3)`
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उत्तर
We know that rationalization factor for `7 + 4sqrt3` is `7 - 4sqrt3`. We will multiply numerator and denominator of the given expression `(5 + 2sqrt3)/(7 + 4sqrt3)` by `7 - 4sqrt3` to get
`(5 + 2sqrt3)/(7 + 4sqrt3) xx (7 - 4sqrt3)/(7 - 4sqrt3) = (5xx7 - 5 xx 4sqrt3 + 2 xx 7 xx sqrt3 - 2 xx 4 xx (sqrt3)^2)/((7)^2 - (4sqrt3)^2)`
`= (35 - 20sqrt3 + 14sqrt3 - 8 xx 3)/(49 - 49)`
`= (11 - 6sqrt3)/1`
`= 11 - 6sqrt3`
Hence the given expression is simplified to `11 - 6sqrt3`
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संबंधित प्रश्न
Classify the following numbers as rational or irrational:
`2-sqrt5`
Rationalise the denominator of the following:
`1/sqrt7`
Simplify the following expressions:
`(2sqrt5 + 3sqrt2)^2`
Rationalise the denominator of the following:
`3/(2sqrt5)`
Rationalise the denominator of the following
`(sqrt3 + 1)/sqrt2`
Find the value to three places of decimals of the following. It is given that
`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
`(sqrt10 + sqrt15)/sqrt2`
`
Find the value to three places of decimals of the following. It is given that
`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
`(sqrt2 - 1)/sqrt5`
Simplify:
`2/(sqrt5 + sqrt3) + 1/(sqrt3 + sqrt2) - 3/(sqrt5 + sqrt2)`
Simplify the following:
`(sqrt(3) - sqrt(2))^2`
Simplify the following:
`root(4)(81) - 8root(3)(216) + 15root(5)(32) + sqrt(225)`
