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प्रश्न
Simplify by rationalising the denominator in the following.
`(3sqrt(5) + sqrt(7))/(3sqrt(5) - sqrt(7)`
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उत्तर
`(3sqrt(5) + sqrt(7))/(3sqrt(5) - sqrt(7)`
= `(3sqrt(5) + sqrt(7))/(3sqrt(5) - sqrt(7)) xx (3sqrt(5) + sqrt(7))/(3sqrt(5) + sqrt(7)`
= `((3sqrt(5) + sqrt(7))^2)/((3sqrt(5))^2 - (sqrt(7))^2`
= `(45 + 7 + 6sqrt(35))/(45 - 7)`
= `(52 + 6sqrt(35))/(38)`
= `(26 + 3sqrt(35))/(19)`
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संबंधित प्रश्न
Rationalise the denominators of : `3/[ sqrt5 + sqrt2 ]`
Rationalise the denominators of : `[ sqrt3 - sqrt2 ]/[ sqrt3 + sqrt2 ]`
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(6))/(5 - sqrt(6)`
Simplify by rationalising the denominator in the following.
`(2sqrt(3) - sqrt(6))/(2sqrt(3) + sqrt(6)`
If x = `((2 + sqrt(5)))/((2 - sqrt(5))` and y = `((2 - sqrt(5)))/((2 + sqrt(5))`, show that (x2 - y2) = `144sqrt(5)`.
If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) + 1)`, 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)`
Draw a line segment of length `sqrt5` cm.
Show that:
`(4 - sqrt5)/(4 + sqrt5) + 2/(5 + sqrt3) + (4 + sqrt5)/(4 - sqrt5) + 2/(5 - sqrt3) = 52/11`
