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प्रश्न
Simplify by rationalising the denominator in the following.
`(2)/(3 + sqrt(7)`
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उत्तर
`(2)/(3 + sqrt(7)`
= `(2)/(3 + sqrt(7)) xx (3 - sqrt(7))/(3 - sqrt(7)`
= `(2(3 - sqrt(7)))/((3)^2 - (sqrt(7))^2)`
= `(2(3 - sqrt(7)))/(9 - 7)`
= `(2(3 - sqrt(7)))/(2)`
= 3 - `sqrt(7)`
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संबंधित प्रश्न
Rationalize the denominator.
`1/(sqrt 7 + sqrt 2)`
Rationalise the denominators of : `[ 2 - √3 ]/[ 2 + √3 ]`
Rationalise the denominators of : `[ √3 + 1 ]/[ √3 - 1 ]`
Simplify :
` 22/[2sqrt3 + 1] + 17/[ 2sqrt3 - 1]`
Simplify the following
`(sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3)) + (sqrt(5) - sqrt(3))/(sqrt(5) + sqrt(3)`
In the following, find the values of a and b:
`(5 + 2sqrt(3))/(7 + 4sqrt(3)) = "a" + "b"sqrt(3)`
In the following, find the values of a and b:
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = "a" - "b"sqrt(6)`
In the following, find the value of a and b:
`(7 + sqrt(5))/(7 - sqrt(5)) - (7 - sqrt(5))/(7 + sqrt(5)) = "a" + "b"sqrt(5)`
If x = `(7 + 4sqrt(3))`, find the values of :
`(x + (1)/x)^2`
Show that: `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + (2 sqrt3)/(sqrt3 - sqrt2) = 11`
