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प्रश्न
Simplify by rationalising the denominator in the following.
`(4 + sqrt(8))/(4 - sqrt(8)`
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उत्तर
`(4 + sqrt(8))/(4 - sqrt(8)`
= `(4 + sqrt(8))/(4 - sqrt(8)) xx (4 + sqrt(8))/(4 + sqrt(8)`
= `((4 + sqrt(8))^2)/((4)^2 - (sqrt(8))^2`
= `(16 + 8 + 8sqrt(8))/(16 - 18)`
= `(24 + 8sqrt(8))/(8)`
= 3 + `sqrt(8)`
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संबंधित प्रश्न
Rationalize the denominator.
`12/(4sqrt3 - sqrt 2)`
Rationalise the denominators of : `[ √3 + 1 ]/[ √3 - 1 ]`
Simplify:
`sqrt2/[sqrt6 - sqrt2] - sqrt3/[sqrt6 + sqrt2]`
Simplify by rationalising the denominator in the following.
`(1)/(5 + sqrt(2))`
Simplify by rationalising the denominator in the following.
`(2)/(3 + sqrt(7)`
If x = `(7 + 4sqrt(3))`, find the value of
`sqrt(x) + (1)/(sqrt(x)`
If x = `(7 + 4sqrt(3))`, find the value of
`x^2 + (1)/x^2`
If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
x2 + y2
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`
