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प्रश्न
Simplify by rationalising the denominator in the following.
`(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6)`
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उत्तर
`(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6)`
= `(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6)) xx (3sqrt(5) + 2sqrt(6))/(3sqrt(5) + 2sqrt(6)`
= `(6sqrt(30) + 24 - 15 - 2sqrt(30))/((3sqrt(5))^2 - (2sqrt(6))^2`
= `(6sqrt(30) + 9 - 2sqrt(30))/(45 - 24)`
= `(4sqrt(30) + 9)/(21)`
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संबंधित प्रश्न
Rationalise the denominators of : `[ sqrt3 - sqrt2 ]/[ sqrt3 + sqrt2 ]`
Simplify : `sqrt18/[ 5sqrt18 + 3sqrt72 - 2sqrt162]`
Simplify by rationalising the denominator in the following.
`(1)/(sqrt(3) + sqrt(2))`
Simplify by rationalising the denominator in the following.
`(3 - sqrt(3))/(2 + sqrt(2)`
In the following, find the values of a and b:
`(1)/(sqrt(5) - sqrt(3)) = "a"sqrt(5) - "b"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 = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
x2 + y2
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:
`(4 - sqrt5)/(4 + sqrt5) + 2/(5 + sqrt3) + (4 + sqrt5)/(4 - sqrt5) + 2/(5 - sqrt3) = 52/11`
