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प्रश्न
Find the value of `6/(sqrt5 - sqrt3)` it being given that `sqrt3 = 1.732` and `sqrt5 = 2.236`
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
Classify the following numbers as rational or irrational:
`2-sqrt5`
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`(3+sqrt3)(2+sqrt2)`
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`(5 + sqrt7)(5 - sqrt7)`
Simplify \[\sqrt{3 + 2\sqrt{2}}\].
If \[x = 3 + 2\sqrt{2}\],then find the value of \[\sqrt{x} - \frac{1}{\sqrt{x}}\].
Classify the following number as rational or irrational:
2π
Rationalise the denominator of the following:
`(2 + sqrt(3))/(2 - sqrt(3))`
Rationalise the denominator of the following:
`(4sqrt(3) + 5sqrt(2))/(sqrt(48) + sqrt(18))`
Find the value of a and b in the following:
`(3 - sqrt(5))/(3 + 2sqrt(5)) = asqrt(5) - 19/11`
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.
`4/sqrt(3)`
