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प्रश्न
Rationalize the denominator.
`4/(7+ 4 sqrt3)`
उत्तर
`4/(7+ 4 sqrt3)`
`= 4/(7+ 4 sqrt3) xx (7- 4 sqrt3)/(7 - 4 sqrt3) `
`= (4(7- 4 sqrt3))/((7)^2 - (4 sqrt 3)^2)` ....`[(a + b)(a - b) = a^2 - b^2]`
`= (4(7- 4 sqrt3)) /(49 - 48)`
`= 28 - 16 sqrt 3`
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संबंधित प्रश्न
Rationalise the denominators of : `[ 2 - √3 ]/[ 2 + √3 ]`
Rationalise the denominators of : `[ √3 + 1 ]/[ √3 - 1 ]`
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`(1)/(5 + sqrt(2))`
Simplify by rationalising the denominator in the following.
`(sqrt(15) + 3)/(sqrt(15) - 3)`
Simplify by rationalising the denominator in the following.
`(3sqrt(5) + sqrt(7))/(3sqrt(5) - sqrt(7)`
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)`
If x = `(7 + 4sqrt(3))`, find the values of :
`(x + (1)/x)^2`
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`
Show that: `x^3 + 1/x^3 = 52`, if x = 2 + `sqrt3`
