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प्रश्न
Find the value of `6/(sqrt5 - sqrt3)` it being given that `sqrt3 = 1.732` and `sqrt5 = 2.236`
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उत्तर
We know that rationalization factor for `sqrt5 - sqrt3` is `sqrt5 + sqrt3`. We will multiply denominator and numerator of the given expression `6/(sqrt5 - sqrt3)` by `sqrt5 + sqrt3` to get
`6/(sqrt5 - sqrt3) xx (sqrt5 + sqrt3)/(sqrt5 + sqrt3) = (6sqrt5 + 6sqrt3)/((sqrt5)^2 - (sqrt3)^3)`
`= (6sqrt5 + 6sqrt3)/(5 - 3)`
`= (6sqrt5 + 6sqrt3)/2`
`= 3sqrt5 + 3sqrt3`
Putting the values of `sqrt5` and `sqrt3` we get
`3sqrt5 + 3sqrt3 = 3(2.236) + 3(1.732)`
= 6.708 + 5.196
= 11.904
Hence value of the given expression is 11.904
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संबंधित प्रश्न
Express the following with rational denominator:
`(sqrt3 + 1)/(2sqrt2 - sqrt3)`
In the following determine rational numbers a and b:
`(5 + 3sqrt3)/(7 + 4sqrt3) = a + bsqrt3`
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Simplify: \[\frac{7 + 3\sqrt{5}}{3 + \sqrt{5}} - \frac{7 - 3\sqrt{5}}{3 - \sqrt{5}}\]
Write the reciprocal of \[5 + \sqrt{2}\].
If \[a = \sqrt{2} + 1\],then find the value of \[a - \frac{1}{a}\].
Simplify the following:
`4sqrt(28) ÷ 3sqrt(7) ÷ root(3)(7)`
Rationalise the denominator of the following:
`2/(3sqrt(3)`
Find the value of a and b in the following:
`(5 + 2sqrt(3))/(7 + 4sqrt(3)) = a - 6sqrt(3)`
Rationalise the denominator in the following and hence evaluate by taking `sqrt(2) = 1.414, sqrt(3) = 1.732` and `sqrt(5) = 2.236`, upto three places of decimal.
`6/sqrt(6)`
