Advertisements
Advertisements
Question
Simplify the following :
`(3sqrt(2))/(sqrt(6) - sqrt(3)) - (4sqrt(3))/(sqrt(6) - sqrt(2)) + (2sqrt(3))/(sqrt(6) + 2)`
Advertisements
Solution
`(3sqrt(2))/(sqrt(6) - sqrt(3)) - (4sqrt(3))/(sqrt(6) - sqrt(2)) + (2sqrt(3))/(sqrt(6) + 2)`
Rationalizing the denominator of each term, we have
= `(3sqrt(2)(sqrt(6) + sqrt(3)))/((sqrt(6) - sqrt(3))(sqrt(6) + sqrt(3))) - (4sqrt(3)(sqrt(6) + sqrt(2)))/((sqrt(6) - sqrt(2))(sqrt(6) + sqrt(2))) + (2sqrt(3)(sqrt(6) - 2))/((sqrt(6) + 2)(sqrt(6) - 2))`
= `(3sqrt(12) + 3sqrt(6))/(6 - 3) - (4sqrt(18) + 4sqrt(6))/(6 - 2) + (2sqrt(18) - 4sqrt(3))/(2)`
= `(3sqrt(12) + 3sqrt(6))/(3) - (4sqrt(18) + 4sqrt(6))/(4) + (2sqrt(18) - 4sqrt(3))/(2)`
= `sqrt(12) + sqrt(6) - sqrt(18) - sqrt(6) + sqrt(18) - 2sqrt(3)`
= `sqrt(12) - 2sqrt(3)`
= `2sqrt(3) - 2sqrt(3)`
= 0
APPEARS IN
RELATED QUESTIONS
Rationalize the denominator.
`(sqrt 5 - sqrt 3)/(sqrt 5 + sqrt 3)`
Rationalize the denominator.
`1/(3 sqrt 5 + 2 sqrt 2)`
Rationalise the denominators of:
`[sqrt6 - sqrt5]/[sqrt6 + sqrt5]`
Simplify:
`sqrt2/[sqrt6 - sqrt2] - sqrt3/[sqrt6 + sqrt2]`
Simplify by rationalising the denominator in the following.
`(1)/(5 + sqrt(2))`
Simplify by rationalising the denominator in the following.
`(sqrt(3) + 1)/(sqrt(3) - 1)`
If x = `(7 + 4sqrt(3))`, find the value of
`sqrt(x) + (1)/(sqrt(x)`
If x = `(4 - sqrt(15))`, find the values of
`x + (1)/x`
Evaluate, correct to one place of decimal, the expression `5/(sqrt20 - sqrt10)`, if `sqrt5` = 2.2 and `sqrt10` = 3.2.
Using the following figure, show that BD = `sqrtx`.
