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प्रश्न
Simplify by rationalising the denominator in the following.
`(5sqrt(3) - sqrt(15))/(5sqrt(3) + sqrt(15)`
उत्तर
`(5sqrt(3) - sqrt(15))/(5sqrt(3) + sqrt(15)`
= `(5sqrt(3) - sqrt(15))/(5sqrt(3) + sqrt(15)) xx (5sqrt(3) - sqrt(15))/(5sqrt(3) - sqrt(15)`
= `((5sqrt(3) - sqrt(15))^2)/((5sqrt(3))^2 - (sqrt(15))^2`
= `(75 + 15 - 10sqrt(45))/(75 - 15)`
= `(90 - 10sqrt(45))/(60)`
= `(9 - 1sqrt(45))/(6)`
= `(9 - 3sqrt(5))/(6)`
= `(3 - sqrt(5))/(2)`
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संबंधित प्रश्न
Rationalize the denominator.
`2/(3 sqrt 7)`
Rationalise the denominators of : `(2sqrt3)/sqrt5`
Rationalise the denominators of : `1/(sqrt3 - sqrt2 )`
Simplify by rationalising the denominator in the following.
`(2)/(3 + sqrt(7)`
Simplify the following :
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2)`
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^3 + (1)/x^3`
If x = `(4 - sqrt(15))`, find the values of
`x^3 + (1)/x^3`
Draw a line segment of length `sqrt5` cm.
Show that: `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + (2 sqrt3)/(sqrt3 - sqrt2) = 11`
