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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
Rationalize the denominator.
`4/(7+ 4 sqrt3)`
Simplify by rationalising the denominator in the following.
`(1)/(sqrt(3) + sqrt(2))`
Simplify by rationalising the denominator in the following.
`(42)/(2sqrt(3) + 3sqrt(2)`
Simplify the following
`(sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3)) + (sqrt(5) - sqrt(3))/(sqrt(5) + sqrt(3)`
In the following, find the values of a and b:
`(7sqrt(3) - 5sqrt(2))/(4sqrt(3) + 3sqrt(2)) = "a" - "b"sqrt(6)`
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)`
If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) - 1)`, find the values of
x2 - y2 + xy
If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
x2 + y2
If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
x3 + y3
Show that:
`(4 - sqrt5)/(4 + sqrt5) + 2/(5 + sqrt3) + (4 + sqrt5)/(4 - sqrt5) + 2/(5 - sqrt3) = 52/11`
