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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
Simplify:
`sqrt2/[sqrt6 - sqrt2] - sqrt3/[sqrt6 + sqrt2]`
Simplify by rationalising the denominator in the following.
`(1)/(sqrt(3) + sqrt(2))`
Simplify by rationalising the denominator in the following.
`(sqrt(3) + 1)/(sqrt(3) - 1)`
Simplify by rationalising the denominator in the following.
`(5 + sqrt(6))/(5 - sqrt(6)`
Simplify the following :
`sqrt(6)/(sqrt(2) + sqrt(3)) + (3sqrt(2))/(sqrt(6) + sqrt(3)) - (4sqrt(3))/(sqrt(6) + sqrt(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)`
In the following, find the value of a and b:
`(sqrt(3) - 1)/(sqrt(3) + 1) + (sqrt(3) + 1)/(sqrt(3) - 1) = "a" + "b"sqrt(3)`
If x = `(7 + 4sqrt(3))`, find the value of
`sqrt(x) + (1)/(sqrt(x)`
If x = `sqrt3 - sqrt2`, find the value of:
(i) `x + 1/x`
(ii) `x^2 + 1/x^2`
(iii) `x^3 + 1/x^3`
(iv) `x^3 + 1/x^3 - 3(x^2 + 1/x^2) + x + 1/x`
Show that: `x^3 + 1/x^3 = 52`, if x = 2 + `sqrt3`
