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प्रश्न
Rationalise the denominator of the following:
`sqrt(6)/(sqrt(2) + sqrt(3))`
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उत्तर
Let `E = sqrt(6)/(sqrt(2) + sqrt(3))`
For rationalising the denominator, multiplying numerator and denominator by `sqrt(2) - sqrt(3)`,
`E = sqrt(6)/(sqrt(2) + sqrt(3)) xx (sqrt(2) - sqrt(3))/(sqrt(2) - sqrt(3))`
= `(sqrt(6)(sqrt(2) - sqrt(3)))/((sqrt(2))^2 - (sqrt(3))^2)` ...[Using identity, (a – b)(a + b) = a2 – b2]
= `(sqrt(6) (sqrt(2) - sqrt(3)))/(2 - 3)`
= `(sqrt(6)(sqrt(2) - sqrt(3)))/(-1)`
= `sqrt(6)(sqrt(3) - sqrt(2))`
= `sqrt(18) - sqrt(12)`
= `sqrt(9 xx 2) - sqrt(4 xx 3)`
= `3sqrt(2) - 2sqrt(3)`
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संबंधित प्रश्न
Simplify the following expressions:
`(3 + sqrt3)(5 - sqrt2)`
Simplify the following expressions:
`(5 + sqrt7)(5 - sqrt7)`
Simplify the following expressions:
`(sqrt3 + sqrt7)^2`
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`
`2/sqrt3`
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`
`(sqrt5 + 1)/sqrt2`
Write the reciprocal of \[5 + \sqrt{2}\].
Simplify the following:
`sqrt(45) - 3sqrt(20) + 4sqrt(5)`
Rationalise the denominator of the following:
`(3sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3))`
Find the value of a and b in the following:
`(3 - sqrt(5))/(3 + 2sqrt(5)) = asqrt(5) - 19/11`
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.
`1/(sqrt(3) + sqrt(2))`
