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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 expression:
`(3+sqrt3)(2+sqrt2)`
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`(sqrt3 + sqrt7)^2`
Rationalise the denominator of the following
`sqrt2/sqrt5`
Rationalise the denominator of the following
`(3sqrt2)/sqrt5`
Rationales the denominator and simplify:
`(1 + sqrt2)/(3 - 2sqrt2)`
Simplify:
`2/(sqrt5 + sqrt3) + 1/(sqrt3 + sqrt2) - 3/(sqrt5 + sqrt2)`
In the following determine rational numbers a and b:
`(4 + 3sqrt5)/(4 - 3sqrt5) = a + bsqrt5`
Find the values the following correct to three places of decimals, it being given that `sqrt2 = 1.4142`, `sqrt3 = 1.732`, `sqrt5 = 2.2360`, `sqrt6 = 2.4495` and `sqrt10 = 3.162`
`(1 + sqrt2)/(3 - 2sqrt2)`
If \[a = \sqrt{2} + 1\],then find the value of \[a - \frac{1}{a}\].
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.
`6/sqrt(6)`
