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प्रश्न
Rationalise the denominators of : `[ sqrt3 - sqrt2 ]/[ sqrt3 + sqrt2 ]`
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उत्तर
`[ sqrt3 - sqrt2 ]/[ sqrt3 + sqrt2 ] xx [ sqrt3 - sqrt2 ]/[ sqrt3 - sqrt2 ]`
= ` (sqrt3 - sqrt2 )^2/[(sqrt3)^2 - (sqrt2)^2]`
= `[ 3 + 2 - 2sqrt6 ]/[ 3 - 2 ]`
= 5 - 2√6
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संबंधित प्रश्न
Rationalise the denominators of:
`[sqrt6 - sqrt5]/[sqrt6 + sqrt5]`
Simplify by rationalising the denominator in the following.
`(3sqrt(5) + sqrt(7))/(3sqrt(5) - sqrt(7)`
Simplify the following :
`(6)/(2sqrt(3) - sqrt(6)) + sqrt(6)/(sqrt(3) + sqrt(2)) - (4sqrt(3))/(sqrt(6) - sqrt(2)`
If `(sqrt(2.5) - sqrt(0.75))/(sqrt(2.5) + sqrt(0.75)) = "p" + "q"sqrt(30)`, find the values of p and q.
In the following, find the values of a and b:
`(5 + 2sqrt(3))/(7 + 4sqrt(3)) = "a" + "b"sqrt(3)`
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 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
`(1)/x`
If x = `(4 - sqrt(15))`, find the values of:
`(x + (1)/x)^2`
If x = `((2 + sqrt(5)))/((2 - sqrt(5))` and y = `((2 - sqrt(5)))/((2 + sqrt(5))`, show that (x2 - y2) = `144sqrt(5)`.
