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प्रश्न
Rationalize the denominator.
`1/(sqrt 7 + sqrt 2)`
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उत्तर
`1/(sqrt 7 + sqrt 2)`
`= 1/(sqrt 7 + sqrt 2) xx (sqrt 7 - sqrt 2)/(sqrt 7 - sqrt 2)`
`= (sqrt 7 - sqrt 2)/((sqrt 7)^2 - (sqrt 2)^2)` ....`[(a + b)(a - b) = a^2- b^2]`
`= (sqrt 7 - sqrt 2)/(7-2)`
`= (sqrt 7 - sqrt 2)/5`
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संबंधित प्रश्न
Rationalise the denominators of : `(2sqrt3)/sqrt5`
Rationalise the denominators of : `1/(sqrt3 - sqrt2 )`
Simplify by rationalising the denominator in the following.
`(5)/(sqrt(7) - sqrt(2))`
Simplify by rationalising the denominator in the following.
`(sqrt(3) + 1)/(sqrt(3) - 1)`
Simplify by rationalising the denominator in the following.
`(3 - sqrt(3))/(2 + sqrt(2)`
Simplify by rationalising the denominator in the following.
`(3sqrt(5) + sqrt(7))/(3sqrt(5) - sqrt(7)`
Simplify the following
`(sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3)) + (sqrt(5) - sqrt(3))/(sqrt(5) + sqrt(3)`
Simplify the following :
`(3sqrt(2))/(sqrt(6) - sqrt(3)) - (4sqrt(3))/(sqrt(6) - sqrt(2)) + (2sqrt(3))/(sqrt(6) + 2)`
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:
`(3 + sqrt(7))/(3 - sqrt(7)) = "a" + "b"sqrt(7)`
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 = `(7 + 4sqrt(3))`, find the value of
`sqrt(x) + (1)/(sqrt(x)`
If x = `(7 + 4sqrt(3))`, find the value of `x^3 + (1)/x^3`.
If x = `(4 - sqrt(15))`, find the values of
`x^2 + (1)/x^2`
If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of
x3 + y3
If x = `sqrt3 - sqrt2`, find the value of:
(i) `x + 1/x`
(ii) `x^2 + 1/x^2`
(iii) `x^3 + 1/x^3`
(iv) `x^3 + 1/x^3 - 3(x^2 + 1/x^2) + x + 1/x`
Draw a line segment of length `sqrt5` cm.
Show that: `x^2 + 1/x^2 = 34,` if x = 3 + `2sqrt2`
