Advertisements
Advertisements
Question
Rationalize the denominator.
`1/(sqrt 7 + sqrt 2)`
Advertisements
Solution
`1/(sqrt 7 + sqrt 2)`
`= 1/(sqrt 7 + sqrt 2) xx (sqrt 7 - sqrt 2)/(sqrt 7 - sqrt 2)`
`= (sqrt 7 - sqrt 2)/((sqrt 7)^2 - (sqrt 2)^2)` ....`[(a + b)(a - b) = a^2- b^2]`
`= (sqrt 7 - sqrt 2)/(7-2)`
`= (sqrt 7 - sqrt 2)/5`
APPEARS IN
RELATED QUESTIONS
Rationalize the denominator.
`2/(3 sqrt 7)`
Rationalize the denominator.
`1/(3 sqrt 5 + 2 sqrt 2)`
Rationalize the denominator.
`12/(4sqrt3 - sqrt 2)`
Rationalise the denominators of : `(2sqrt3)/sqrt5`
Rationalise the denominators of : `[ √3 + 1 ]/[ √3 - 1 ]`
Simplify :
` 22/[2sqrt3 + 1] + 17/[ 2sqrt3 - 1]`
Simplify:
`sqrt2/[sqrt6 - sqrt2] - sqrt3/[sqrt6 + sqrt2]`
Simplify : `sqrt18/[ 5sqrt18 + 3sqrt72 - 2sqrt162]`
Simplify by rationalising the denominator in the following.
`(42)/(2sqrt(3) + 3sqrt(2)`
Simplify by rationalising the denominator in the following.
`(5sqrt(3) - sqrt(15))/(5sqrt(3) + sqrt(15)`
Simplify the following
`(4 + sqrt(5))/(4 - sqrt(5)) + (4 - sqrt(5))/(4 + sqrt(5)`
Simplify the following :
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2)`
If `(sqrt(2.5) - sqrt(0.75))/(sqrt(2.5) + sqrt(0.75)) = "p" + "q"sqrt(30)`, find the values of p and q.
In the following, find the values of a and b:
`(1)/(sqrt(5) - sqrt(3)) = "a"sqrt(5) - "b"sqrt(3)`
In the following, find the values of a and b:
`(sqrt(11) - sqrt(7))/(sqrt(11) + sqrt(7)) = "a" - "b"sqrt(77)`
In the following, find the value of a and b:
`(sqrt(3) - 1)/(sqrt(3) + 1) + (sqrt(3) + 1)/(sqrt(3) - 1) = "a" + "b"sqrt(3)`
If x = `(7 + 4sqrt(3))`, find the value of
`sqrt(x) + (1)/(sqrt(x)`
If x = `(4 - sqrt(15))`, find the values of
`x^3 + (1)/x^3`
Simplify:
`(sqrt(x^2 + y^2) - y)/(x - sqrt(x^2 - y^2)) ÷ (sqrt(x^2 - y^2) + x)/(sqrt(x^2 + y^2) + y)`
