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प्रश्न
Simplify by rationalising the denominator in the following.
`(sqrt(7) - sqrt(5))/(sqrt(7) + sqrt(5)`
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उत्तर
`(sqrt(7) - sqrt(5))/(sqrt(7) + sqrt(5)`
= `(sqrt(7) - sqrt(5))/(sqrt(7) + sqrt(5)) xx (sqrt(7) - sqrt(5))/(sqrt(7) - sqrt(5)`
= `(sqrt(7) - sqrt(5))^2/((sqrt(7))^2 - (sqrt(5))^2`
= `(7 + 5 - 2sqrt(35))/(7 - 5)`
= `(12 - 2sqrt(35))/(2)`
= 6 - `sqrt(35)`
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संबंधित प्रश्न
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Simplify by rationalising the denominator in the following.
`(3sqrt(5) + sqrt(7))/(3sqrt(5) - sqrt(7)`
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(11) - sqrt(7))/(sqrt(11) + sqrt(7)) = "a" - "b"sqrt(77)`
In the following, find the values of a and b:
`(7sqrt(3) - 5sqrt(2))/(4sqrt(3) + 3sqrt(2)) = "a" - "b"sqrt(6)`
If x = `(4 - sqrt(15))`, find the values of
`x + (1)/x`
Draw a line segment of length `sqrt3` cm.
Show that:
`(4 - sqrt5)/(4 + sqrt5) + 2/(5 + sqrt3) + (4 + sqrt5)/(4 - sqrt5) + 2/(5 - sqrt3) = 52/11`
Show that: `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + (2 sqrt3)/(sqrt3 - sqrt2) = 11`
