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प्रश्न
Simplify:
`(5 + sqrt3)/(5 - sqrt3) + (5 - sqrt3)/(5 + sqrt3)`
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उत्तर
We know that rationalization factor for `sqrt5 - sqrt3` and `sqrt5 + sqrt3` are `sqrt5 + sqrt3` and `sqrt5 - sqrt3` respectively.
We will multiply numerator and denominator of the given expression `(sqrt5 + sqrt3)/(sqrt5 - sqrt3)` and `(sqrt5 - sqrt3)/(sqrt5 + sqrt3)` by `sqrt5 + sqrt3` and `sqrt5 + sqrt3` respectively, to get
`(sqrt5 + sqrt3)/(sqrt5 - sqrt3) xx (sqrt5 + sqrt3)/(sqrt5 + sqrt3) + (sqrt5 - sqrt3)/(sqrt5 + sqrt3) xx (sqrt5 - sqrt3)/(sqrt5 - sqrt3) = ((sqrt5)^2 + (sqrt3)^2 + 2 xx sqrt5 xx sqrt3)/((sqrt5)^2- (sqrt3)^2)`
`(5 + 3 + 2sqrt15)/(5- 3) + (5 + 3 - 2sqrt15)/(5 - 3)`
`= (5 + 3 + 2sqrt15 + 5 + 3 - 2sqrt15)/2`
= 16/2
= 8
Hence the given expression is simplified to 8
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संबंधित प्रश्न
Express of the following with rational denominator:
`1/(sqrt6 - sqrt5)`
Express the following with rational denominator:
`1/(2sqrt5 - sqrt3)`
Express the following with rational denominator:
`(3sqrt2 + 1)/(2sqrt5 - 3)`
Rationales the denominator and simplify:
`(3 - sqrt2)/(3 + sqrt2)`
Rationales the denominator and simplify:
`(2sqrt6 - sqrt5)/(3sqrt5 - 2sqrt6)`
Rationales the denominator and simplify:
`(2sqrt3 - sqrt5)/(2sqrt2 + 3sqrt3)`
The rationalisation factor of \[\sqrt{3}\] is
Simplify the following:
`sqrt(24)/8 + sqrt(54)/9`
Rationalise the denominator of the following:
`(sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2))`
Rationalise the denominator in the following and hence evaluate by taking `sqrt(2) = 1.414, sqrt(3) = 1.732` and `sqrt(5) = 2.236`, upto three places of decimal.
`4/sqrt(3)`
