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प्रश्न
Rationalize the denominator.
`3/(2 sqrt 5 - 3 sqrt 2)`
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उत्तर
`3/(2 sqrt 5 - 3 sqrt 2)`
`= 3/(2 sqrt 5 - 3 sqrt 2) xx (2 sqrt 5 + 3 sqrt 2)/(2 sqrt 5 + 3 sqrt 2)`
`= (3(2 sqrt 5 + 3 sqrt 2))/((2 sqrt 5)^2 - (3 sqrt 2)^2)`
.....`[("a" + "b")("a" - "b") = "a"^2 - "b"^2]`
`= (3(2 sqrt 5 + 3 sqrt 2))/(4 xx 5 - 9 xx 2)`
`= (3(2 sqrt 5 + 3 sqrt 2))/(20 - 18)`
`= (3(2 sqrt 5 + 3 sqrt 2))/2`
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संबंधित प्रश्न
Rationalize the denominator.
`2/(3 sqrt 7)`
Rationalise the denominators of : `3/sqrt5`
Rationalise the denominators of : `[ √3 + 1 ]/[ √3 - 1 ]`
If `sqrt2` = 1.4 and `sqrt3` = 1.7, find the value of `(2 - sqrt3)/(sqrt3).`
Simplify by rationalising the denominator in the following.
`(5)/(sqrt(7) - sqrt(2))`
Simplify by rationalising the denominator in the following.
`(3sqrt(5) + sqrt(7))/(3sqrt(5) - sqrt(7)`
Simplify the following
`(sqrt(7) - sqrt(3))/(sqrt(7) + sqrt(3)) - (sqrt(7) + sqrt(3))/(sqrt(7) - sqrt(3)`
Simplify the following
`(sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3)) + (sqrt(5) - sqrt(3))/(sqrt(5) + sqrt(3)`
Simplify the following :
`(4sqrt(3))/((2 - sqrt(2))) - (30)/((4sqrt(3) - 3sqrt(2))) - (3sqrt(2))/((3 + 2sqrt(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:
`(sqrt(11) - sqrt(7))/(sqrt(11) + sqrt(7)) = "a" - "b"sqrt(77)`
If x = `(4 - sqrt(15))`, find the values of
`x + (1)/x`
If x = `(4 - sqrt(15))`, find the values of
`x^2 + (1)/x^2`
If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) + 1)`, find the values of
x2 + y2
If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) + 1)`, find the values of
x3 + y3
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: `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + (2 sqrt3)/(sqrt3 - sqrt2) = 11`
