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प्रश्न
Write the reciprocal of \[5 + \sqrt{2}\].
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उत्तर
Given that,`5+sqrt2` it’s reciprocal is given as
`1/(5+sqrt2)`
It can be simplified by rationalizing the denominator. The rationalizing factor of `5+sqrt2` is ` 5 - sqrt2`, we will multiply numerator and denominator of the given expression `1/(5+sqrt2)`by, `5-sqrt2` to get
`1/(5+sqrt2) xx (5-sqrt2)/(5-sqrt2) = (5-sqrt2)/((5)^2 - (sqrt2)^2)`
`= (5-sqrt2) /( 25-2)`
` = (5- sqrt2 ) / 23 `
Hence reciprocal of the given expression is `(5- sqrt2 ) / 23 `.
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संबंधित प्रश्न
Rationalise the denominator of the following:
`1/sqrt7`
Simplify the following expressions:
`(2sqrt5 + 3sqrt2)^2`
Simplify \[\sqrt{3 - 2\sqrt{2}}\].
Rationalise the denominator of the following:
`1/(sqrt7-2)`
Rationalise the denominator of the following:
`1/(sqrt7-sqrt6)`
Rationalise the denominator of the following:
`sqrt(40)/sqrt(3)`
Rationalise the denominator of the following:
`(sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2))`
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:
`[((625)^(-1/2))^((-1)/4)]^2`
Simplify:
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2))`
