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प्रश्न
Simplify by rationalising the denominator in the following.
`(sqrt(15) + 3)/(sqrt(15) - 3)`
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उत्तर
`(sqrt(15) + 3)/(sqrt(15) - 3)`
= `(sqrt(15) + 3)/(sqrt(15) - 3) xx (sqrt(15) + 3)/(sqrt(15) + 3)`
= `(sqrt(15) + 3)^2/((sqrt(15))^2 - (3)^2`
= `(15 + 9 + 6sqrt(15))/(15 - 9)`
= `(24 + 6sqrt(15))/(6)`
= 4 + `sqrt(15)`
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संबंधित प्रश्न
Simplify by rationalising the denominator in the following.
`(2)/(3 + sqrt(7)`
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.
`(sqrt(3) - 1)/(sqrt(3) + 1) = "a" + "b"sqrt(3)`
In the following, find the values of a and b:
`(1)/(sqrt(5) - sqrt(3)) = "a"sqrt(5) - "b"sqrt(3)`
If x = `(4 - sqrt(15))`, find the values of:
`(x + (1)/x)^2`
If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) + 1)`, find the values of
x3 + y3
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: `x^3 + 1/x^3 = 52`, if x = 2 + `sqrt3`
