Advertisements
Advertisements
प्रश्न
Simplify the following :
`(3sqrt(2))/(sqrt(6) - sqrt(3)) - (4sqrt(3))/(sqrt(6) - sqrt(2)) + (2sqrt(3))/(sqrt(6) + 2)`
Advertisements
उत्तर
`(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
संबंधित प्रश्न
Rationalize the denominator.
`3/(2 sqrt 5 - 3 sqrt 2)`
Rationalise the denominators of : `[ 2√5 + 3√2 ]/[ 2√5 - 3√2 ]`
Rationalise the denominator of `1/[ √3 - √2 + 1]`
Simplify by rationalising the denominator in the following.
`(sqrt(7) - sqrt(5))/(sqrt(7) + sqrt(5)`
Simplify the following
`(sqrt(5) - 2)/(sqrt(5) + 2) - (sqrt(5) + 2)/(sqrt(5) - 2)`
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)`
If x = `(7 + 4sqrt(3))`, find the value of
`sqrt(x) + (1)/(sqrt(x)`
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)`
Show that Negative of an irrational number is irrational.
Show that: `x^2 + 1/x^2 = 34,` if x = 3 + `2sqrt2`
