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प्रश्न
Rationalise the denominator of the following
`(sqrt2 + sqrt5)/3`
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उत्तर
We know that rationalization factor for `1/sqrta` is `sqrta`. We will multiply numerator and denominator of the given expression `(sqrt2 + sqrt5)/sqrt3` by `sqrt3` to get
`(sqrt2 + sqrt5)/sqrt3 " by " sqrt3` to get
`(sqrt2 + sqrt5)/sqrt3 xx sqrt3/sqrt3 = (sqrt2 xx sqrt3 + sqrt5 xx sqrt3)/(sqrt3 xx sqrt3)`
`= (sqrt6 + sqrt15)/3`
Hence the given expression is simplified to `(sqrt6 +sqrt15)/3`
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संबंधित प्रश्न
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`
Rationales the denominator and simplify:
`(2sqrt6 - sqrt5)/(3sqrt5 - 2sqrt6)`
Rationales the denominator and simplify:
`(4sqrt3 + 5sqrt2)/(sqrt48 + sqrt18)`
In the following determine rational numbers a and b:
`(sqrt3 - 1)/(sqrt3 + 1) = a - bsqrt3`
Simplify: \[\frac{3\sqrt{2} - 2\sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}\]
Write the value of \[\left( 2 + \sqrt{3} \right) \left( 2 - \sqrt{3} \right) .\]
Write the reciprocal of \[5 + \sqrt{2}\].
If \[x = 2 + \sqrt{3}\] , find the value of \[x + \frac{1}{x}\].
Rationalise the denominator of the following:
`1/(sqrt5+sqrt2)`
Find the value of a and b in the following:
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = 2 - bsqrt(6)`
