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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
Rationalize the denominator.
`2/(3 sqrt 7)`
Rationalize the denominator.
`1/(3 sqrt 5 + 2 sqrt 2)`
Rationalise the denominators of : `[ sqrt3 - sqrt2 ]/[ sqrt3 + sqrt2 ]`
Rationalise the denominators of:
`[sqrt6 - sqrt5]/[sqrt6 + sqrt5]`
Simplify the following :
`(3sqrt(2))/(sqrt(6) - sqrt(3)) - (4sqrt(3))/(sqrt(6) - sqrt(2)) + (2sqrt(3))/(sqrt(6) + 2)`
Simplify the following :
`(6)/(2sqrt(3) - sqrt(6)) + sqrt(6)/(sqrt(3) + sqrt(2)) - (4sqrt(3))/(sqrt(6) - sqrt(2)`
In the following, find the values of a and b:
`(3 + sqrt(7))/(3 - sqrt(7)) = "a" + "b"sqrt(7)`
In the following, find the values of a and b:
`(sqrt(3) - 2)/(sqrt(3) + 2) = "a"sqrt(3) + "b"`
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)`
Show that:
`(4 - sqrt5)/(4 + sqrt5) + 2/(5 + sqrt3) + (4 + sqrt5)/(4 - sqrt5) + 2/(5 - sqrt3) = 52/11`
