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प्रश्न
Simplify by rationalising the denominator in the following.
`(2sqrt(3) - sqrt(6))/(2sqrt(3) + sqrt(6)`
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उत्तर
`(2sqrt(3) - sqrt(6))/(2sqrt(3) + sqrt(6)`
= `(2sqrt(3) - sqrt(6))/(2sqrt(3) + sqrt(6)) xx (2sqrt(3) - sqrt(6))/(2sqrt(3) - sqrt(6)`
= `((2sqrt(3) - sqrt(6))^2)/((2sqrt(3))^2 - (sqrt(6))^2`
= `(12 + 6 - 4sqrt(18))/(12 - 6)`
= `(18 - 4sqrt(18))/(6)`
= `(9 - 2sqrt(18))/(3)`
= `(9 - 6sqrt(2))/(3)`
= 3 - 2`sqrt(2)`
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संबंधित प्रश्न
Rationalise the denominators of : `[ √3 + 1 ]/[ √3 - 1 ]`
Rationalise the denominators of : `[ sqrt3 - sqrt2 ]/[ sqrt3 + sqrt2 ]`
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`(3sqrt(2))/sqrt(5)`
Simplify by rationalising the denominator in the following.
`(5)/(sqrt(7) - sqrt(2))`
Simplify by rationalising the denominator in the following.
`(5sqrt(3) - sqrt(15))/(5sqrt(3) + sqrt(15)`
Simplify by rationalising the denominator in the following.
`(sqrt(12) + sqrt(18))/(sqrt(75) - sqrt(50)`
Simplify the following
`(3)/(5 - sqrt(3)) + (2)/(5 + sqrt(3)`
In the following, find the values of a and b:
`(3 + sqrt(7))/(3 - sqrt(7)) = "a" + "b"sqrt(7)`
If x = `(4 - sqrt(15))`, find the values of
`x + (1)/x`
Show that:
`(4 - sqrt5)/(4 + sqrt5) + 2/(5 + sqrt3) + (4 + sqrt5)/(4 - sqrt5) + 2/(5 - sqrt3) = 52/11`
