Advertisements
Advertisements
Question
Rationalise the denominators of:
`[sqrt6 - sqrt5]/[sqrt6 + sqrt5]`
Advertisements
Solution
`[sqrt6 - sqrt5]/[sqrt6 + sqrt5] xx [sqrt6 - sqrt5]/[sqrt6 - sqrt5]`
= `[(sqrt6 - sqrt5)^2]/[(sqrt6)^2 - (sqrt5)^2]`
= `[(sqrt6)^2 + (sqrt5)^2 - 2(sqrt6 xx sqrt5)]/[(sqrt6)^2 - (sqrt5)^2]`
= `[6 + 5 - 2sqrt30 ]/[(sqrt6)^2 - (sqrt5)^2]`
= `[11 - 2sqrt30 ]/[6 - 5]`
= `11 - 2sqrt30`
APPEARS IN
RELATED QUESTIONS
Rationalize the denominator.
`1/(sqrt 7 + sqrt 2)`
Rationalize the denominator.
`1/sqrt5`
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.
`(2sqrt(3) - sqrt(6))/(2sqrt(3) + sqrt(6)`
Simplify the following
`(sqrt(7) - sqrt(3))/(sqrt(7) + sqrt(3)) - (sqrt(7) + sqrt(3))/(sqrt(7) - sqrt(3)`
If x = `(4 - sqrt(15))`, find the values of
`x^2 + (1)/x^2`
If x = `(4 - sqrt(15))`, find the values of:
`(x + (1)/x)^2`
If x = `((2 + sqrt(5)))/((2 - sqrt(5))` and y = `((2 - sqrt(5)))/((2 + sqrt(5))`, show that (x2 - y2) = `144sqrt(5)`.
Draw a line segment of length `sqrt5` cm.
