Advertisements
Advertisements
Question
Rationalize the denominator.
`1/(3 sqrt 5 + 2 sqrt 2)`
Advertisements
Solution
`1/(3 sqrt 5 + 2 sqrt 2)`
`= 1/((3 sqrt 5 + 2 sqrt 2)) xx ((3 sqrt 5 - 2 sqrt 2))/((3 sqrt 5 - 2 sqrt 2))`
` = ((3 sqrt 5 - 2 sqrt 2))/((3sqrt5)^2 - (2sqrt 2)^2)
...[(a+b)(a-b) = a^2 - b^2]`
`= ((3 sqrt5 - 2 sqrt 2))/(45-8)`
`= (3 sqrt5 - 2 sqrt 2)/37`
APPEARS IN
RELATED QUESTIONS
Rationalize the denominator.
`1/(sqrt 7 + sqrt 2)`
Rationalize the denominator.
`4/(7+ 4 sqrt3)`
Rationalise the denominators of : `(2sqrt3)/sqrt5`
Rationalise the denominators of : `[ 2 - √3 ]/[ 2 + √3 ]`
Rationalise the denominators of : `3/[ sqrt5 + sqrt2 ]`
Rationalise the denominators of : `[ 2√5 + 3√2 ]/[ 2√5 - 3√2 ]`
If `sqrt2` = 1.4 and `sqrt3` = 1.7, find the value of `(2 - sqrt3)/(sqrt3).`
Simplify the following
`(3)/(5 - sqrt(3)) + (2)/(5 + sqrt(3)`
Simplify the following
`(sqrt(5) - 2)/(sqrt(5) + 2) - (sqrt(5) + 2)/(sqrt(5) - 2)`
Simplify the following
`(sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3)) + (sqrt(5) - sqrt(3))/(sqrt(5) + sqrt(3)`
In the following, find the value of a and b:
`(7 + sqrt(5))/(7 - sqrt(5)) - (7 - sqrt(5))/(7 + sqrt(5)) = "a" + "b"sqrt(5)`
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
`x^2 + (1)/x^2`
If x = `(4 - sqrt(15))`, find the values of
`x + (1)/x`
If x = `(4 - sqrt(15))`, find the values of
`x^3 + (1)/x^3`
If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) + 1)`, find the values of
x2 + y2
If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
x2 + y2
If x = `sqrt3 - sqrt2`, find the value of:
(i) `x + 1/x`
(ii) `x^2 + 1/x^2`
(iii) `x^3 + 1/x^3`
(iv) `x^3 + 1/x^3 - 3(x^2 + 1/x^2) + x + 1/x`
Show that: `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + (2 sqrt3)/(sqrt3 - sqrt2) = 11`
