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प्रश्न
Simplify:
`(5 + sqrt3)/(5 - sqrt3) + (5 - sqrt3)/(5 + sqrt3)`
उत्तर
We know that rationalization factor for `sqrt5 - sqrt3` and `sqrt5 + sqrt3` are `sqrt5 + sqrt3` and `sqrt5 - sqrt3` respectively.
We will multiply numerator and denominator of the given expression `(sqrt5 + sqrt3)/(sqrt5 - sqrt3)` and `(sqrt5 - sqrt3)/(sqrt5 + sqrt3)` by `sqrt5 + sqrt3` and `sqrt5 + sqrt3` respectively, to get
`(sqrt5 + sqrt3)/(sqrt5 - sqrt3) xx (sqrt5 + sqrt3)/(sqrt5 + sqrt3) + (sqrt5 - sqrt3)/(sqrt5 + sqrt3) xx (sqrt5 - sqrt3)/(sqrt5 - sqrt3) = ((sqrt5)^2 + (sqrt3)^2 + 2 xx sqrt5 xx sqrt3)/((sqrt5)^2- (sqrt3)^2)`
`(5 + 3 + 2sqrt15)/(5- 3) + (5 + 3 - 2sqrt15)/(5 - 3)`
`= (5 + 3 + 2sqrt15 + 5 + 3 - 2sqrt15)/2`
= 16/2
= 8
Hence the given expression is simplified to 8
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संबंधित प्रश्न
Rationalise the denominator of the following:
`1/sqrt7`
Find the value to three places of decimals of the following. It is given that
`sqrt2 = 1.414`, `sqrt3 = 1.732`, `sqrt5 = 2.236` and `sqrt10 = 3.162`
`(sqrt2 - 1)/sqrt5`
Simplify:
`2/(sqrt5 + sqrt3) + 1/(sqrt3 + sqrt2) - 3/(sqrt5 + sqrt2)`
In the following determine rational numbers a and b:
`(3 + sqrt2)/(3 - sqrt2) = a + bsqrt2`
If \[a = \sqrt{2} + 1\],then find the value of \[a - \frac{1}{a}\].
Write the rationalisation factor of \[\sqrt{5} - 2\].
Classify the following number as rational or irrational:
`1/sqrt2`
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.
`(sqrt(10) - sqrt(5))/2`
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.
`sqrt(2)/(2 + sqrt(2)`
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.
`1/(sqrt(3) + sqrt(2))`
