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प्रश्न
Simplify by rationalising the denominator in the following.
`(3sqrt(5) + sqrt(7))/(3sqrt(5) - sqrt(7)`
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उत्तर
`(3sqrt(5) + sqrt(7))/(3sqrt(5) - sqrt(7)`
= `(3sqrt(5) + sqrt(7))/(3sqrt(5) - sqrt(7)) xx (3sqrt(5) + sqrt(7))/(3sqrt(5) + sqrt(7)`
= `((3sqrt(5) + sqrt(7))^2)/((3sqrt(5))^2 - (sqrt(7))^2`
= `(45 + 7 + 6sqrt(35))/(45 - 7)`
= `(52 + 6sqrt(35))/(38)`
= `(26 + 3sqrt(35))/(19)`
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संबंधित प्रश्न
Rationalize the denominator.
`3/(2 sqrt 5 - 3 sqrt 2)`
Rationalise the denominators of : `3/[ sqrt5 + sqrt2 ]`
Simplify:
`sqrt2/[sqrt6 - sqrt2] - sqrt3/[sqrt6 + sqrt2]`
Simplify by rationalising the denominator in the following.
`(5 + sqrt(6))/(5 - sqrt(6)`
Simplify the following :
`(3sqrt(2))/(sqrt(6) - sqrt(3)) - (4sqrt(3))/(sqrt(6) - sqrt(2)) + (2sqrt(3))/(sqrt(6) + 2)`
Simplify the following :
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2)`
If x = `(4 - sqrt(15))`, find the values of
`(1)/x`
If x = `(4 - sqrt(15))`, find the values of
`x^3 + (1)/x^3`
Simplify:
`(sqrt(x^2 + y^2) - y)/(x - sqrt(x^2 - y^2)) ÷ (sqrt(x^2 - y^2) + x)/(sqrt(x^2 + y^2) + y)`
Show that:
`(4 - sqrt5)/(4 + sqrt5) + 2/(5 + sqrt3) + (4 + sqrt5)/(4 - sqrt5) + 2/(5 - sqrt3) = 52/11`
