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प्रश्न
Simplify by rationalising the denominator in the following.
`(3 - sqrt(3))/(2 + sqrt(2)`
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उत्तर
`(3 - sqrt(3))/(2 + sqrt(2)`
= `(3 - sqrt(3))/(2 + sqrt(2)) xx (2 - sqrt(2))/(2 - sqrt(2)`
= `(3(2 - sqrt(2)) - sqrt(3)(2 - sqrt(2)))/((2)^2 - (sqrt(2))^2)`
= `(6 - 3sqrt(2) - 2sqrt(3) + sqrt(6))/(4 - 2)`
= `(6 - 3sqrt(2) - 2sqrt(3) + sqrt(6))/(2)`
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संबंधित प्रश्न
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`(1)/(5 + sqrt(2))`
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`(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6)`
Simplify the following
`(4 + sqrt(5))/(4 - sqrt(5)) + (4 - sqrt(5))/(4 + sqrt(5)`
In the following, find the values of a and b:
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = "a" - "b"sqrt(6)`
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`(sqrt(3) - 1)/(sqrt(3) + 1) + (sqrt(3) + 1)/(sqrt(3) - 1) = "a" + "b"sqrt(3)`
Evaluate, correct to one place of decimal, the expression `5/(sqrt20 - sqrt10)`, if `sqrt5` = 2.2 and `sqrt10` = 3.2.
Show that:
`(4 - sqrt5)/(4 + sqrt5) + 2/(5 + sqrt3) + (4 + sqrt5)/(4 - sqrt5) + 2/(5 - sqrt3) = 52/11`
