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प्रश्न
Rationalise the denominator of the following:
`1/(sqrt7-sqrt6)`
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उत्तर
The given number is `1/(sqrt7 - sqrt6)`
On rationalising the denominator,
⇒ `1/(sqrt7 - sqrt6) = 1/(sqrt7 - sqrt6) xx (sqrt7 + sqrt6)/(sqrt7 + sqrt6)`
We know that (a + b) (a + b) = a2 - b2
⇒ `1/(sqrt7 - sqrt6) = (sqrt7 + sqrt6)/((sqrt7)^2 - (sqrt6)^2)`
⇒ `1/(sqrt7 - sqrt6) = (sqrt7 + sqrt6)/(7 - 6)`
∴ `1/(sqrt7 - sqrt6) = sqrt7 + sqrt6`
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संबंधित प्रश्न
Simplify the following expression:
`(3+sqrt3)(2+sqrt2)`
Simplify the following expressions:
`(3 + sqrt3)(5 - sqrt2)`
Rationales the denominator and simplify:
`(5 + 2sqrt3)/(7 + 4sqrt3)`
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 \[a - \frac{1}{a}\].
The rationalisation factor of \[\sqrt{3}\] is
Simplify the following:
`(2sqrt(3))/3 - sqrt(3)/6`
Rationalise the denominator of the following:
`16/(sqrt(41) - 5)`
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(10) - sqrt(5))/2`
Simplify:
`(1/27)^((-2)/3)`
