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प्रश्न
Rationalise the denominator of the following:
`1/(sqrt7-2)`
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उत्तर
The given number is `1/(sqrt7 - 2)`
On rationalising the denominator,
⇒ `1/(sqrt7 - 2) = 1/(sqrt7 - 2) xx (sqrt7 + 2)/(sqrt7 + 2)`
We know that (a + b) (a − b) = a2 − b2
⇒ `1/(sqrt7 - 2) = (sqrt7 + 2)/((sqrt7)^2 - (2)^2)`
⇒ `1/(sqrt7 - 2) = (sqrt7 + 2)/(7 - 4)`
∴ `1/(sqrt7 - 2) = (sqrt7 + 2)/3`
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संबंधित प्रश्न
Classify the following numbers as rational or irrational:
`2-sqrt5`
Simplify the following expression:
`(3+sqrt3)(2+sqrt2)`
Rationalise the denominator of the following:
`1/sqrt7`
Rationalise the denominator of each of the following
`3/sqrt5`
Express the following with rational denominator:
`(sqrt3 + 1)/(2sqrt2 - sqrt3)`
Simplify: \[\frac{7 + 3\sqrt{5}}{3 + \sqrt{5}} - \frac{7 - 3\sqrt{5}}{3 - \sqrt{5}}\]
Simplify: \[\frac{3\sqrt{2} - 2\sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}\]
If \[a = \sqrt{2} + 1\],then find the value of \[a - \frac{1}{a}\].
Rationalise the denominator of the following:
`1/(sqrt7-sqrt6)`
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))`
