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प्रश्न
Rationalise the denominator of the following
`(sqrt2 + sqrt5)/3`
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`
`(2 + sqrt3)/3`
Express of the following with rational denominator:
`1/(sqrt6 - sqrt5)`
Express the following with rational denominator:
`(6 - 4sqrt2)/(6 + 4sqrt2)`
If \[x = 2 + \sqrt{3}\] , find the value of \[x + \frac{1}{x}\].
The rationalisation factor of \[\sqrt{3}\] is
Classify the following number as rational or irrational:
`(2sqrt7)/(7sqrt7)`
Rationalise the denominator of the following:
`1/(sqrt5+sqrt2)`
`1/(sqrt(9) - sqrt(8))` is equal to ______.
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.
`sqrt(2)/(2 + sqrt(2)`
Simplify:
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2))`
