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प्रश्न
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`
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उत्तर
We know that rationalization factor of the denominator is `sqrt5`. We will multiply numerator and denominator of the given expression `(sqrt2 - 1)/sqrt5`by `sqrt5` to get
`(sqrt2 - 1)/sqrt5 xx sqrt5/sqrt5 = (sqrt2 xx sqrt5 - sqrt5)/(sqrt5 xx sqrt5)`
`= (sqrt10 - sqrt5)/5`
Putting the value of `sqrt10`and `sqrt5` we get
`(sqrt10 - sqrt5)/5 = (3.162 - 2.236)/5`
`= 0.926/5`
= 0.1852
The value of expression 0.1852 can be round off tp three decimal places as 0.185.
given expression is simplified to 0.185
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संबंधित प्रश्न
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`(sqrt3 + sqrt7)^2`
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`3/sqrt5`
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`(3sqrt2 + 1)/(2sqrt5 - 3)`
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`(2sqrt6 - sqrt5)/(3sqrt5 - 2sqrt6)`
In the following determine rational numbers a and b:
`(5 + 3sqrt3)/(7 + 4sqrt3) = a + bsqrt3`
In the following determine rational numbers a and b:
`(4 + 3sqrt5)/(4 - 3sqrt5) = a + bsqrt5`
Find the values the following correct to three places of decimals, it being given that `sqrt2 = 1.4142`, `sqrt3 = 1.732`, `sqrt5 = 2.2360`, `sqrt6 = 2.4495` and `sqrt10 = 3.162`
`(1 + sqrt2)/(3 - 2sqrt2)`
if `x = (sqrt3 + 1)/2` find the value of `4x^2 +2x^2 - 8x + 7`
Classify the following number as rational or irrational:
`(2sqrt7)/(7sqrt7)`
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)`
