Advertisements
Advertisements
Question
Write the reciprocal of \[5 + \sqrt{2}\].
Advertisements
Solution
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 `.
APPEARS IN
RELATED QUESTIONS
Simplify of the following:
`root(4)1250/root(4)2`
Simplify the following expressions:
`(5 + sqrt7)(5 - sqrt7)`
Rationalise the denominator of the following
`(sqrt3 + 1)/sqrt2`
Rationales the denominator and simplify:
`(5 + 2sqrt3)/(7 + 4sqrt3)`
In the following determine rational numbers a and b:
`(3 + sqrt2)/(3 - sqrt2) = a + bsqrt2`
Simplify \[\sqrt{3 + 2\sqrt{2}}\].
The number obtained on rationalising the denominator of `1/(sqrt(7) - 2)` is ______.
Simplify the following:
`3/sqrt(8) + 1/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.
`6/sqrt(6)`
Simplify:
`64^(-1/3)[64^(1/3) - 64^(2/3)]`
