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
Express of the following with rational denominator:
`1/(sqrt6 - sqrt5)`
Simplify
`1/(2 + sqrt3) + 2/(sqrt5 - sqrt3) + 1/(2 - sqrt5)`
In the following determine rational numbers a and b:
`(4 + 3sqrt5)/(4 - 3sqrt5) = a + bsqrt5`
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 `x= 3 + sqrt8`, find the value of `x^2 + 1/x^2`
Simplify: \[\frac{7 + 3\sqrt{5}}{3 + \sqrt{5}} - \frac{7 - 3\sqrt{5}}{3 - \sqrt{5}}\]
`1/(sqrt(9) - sqrt(8))` is equal to ______.
After rationalising the denominator of `7/(3sqrt(3) - 2sqrt(2))`, we get the denominator as ______.
Rationalise the denominator of the following:
`sqrt(6)/(sqrt(2) + sqrt(3))`
Find the value of a and b in the following:
`(5 + 2sqrt(3))/(7 + 4sqrt(3)) = a - 6sqrt(3)`
