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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`
`3/sqrt10`
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उत्तर
We know that rationalization factor of the denominator is `sqrt10`. We will multiply numberator and denominator of the given expression `3/sqrt10` by `sqrt10to get
`3/sqrt10 xx sqrt10/sqrt10 = (3 xx sqrt10)/(sqrt10 xx sqrt10)`
`= (3sqrt10)/10`
`= (3 xx 3.162)/10`
`= 9.486/10`
= 0.9486
The value of expression 0.9486 can be round off to three decimal places as 0.949.
Hence the given expression is simplified to 0.949.
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संबंधित प्रश्न
Simplify:
`2/(sqrt5 + sqrt3) + 1/(sqrt3 + sqrt2) - 3/(sqrt5 + sqrt2)`
In the following determine rational numbers a and b:
`(sqrt3 - 1)/(sqrt3 + 1) = a - bsqrt3`
Write the reciprocal of \[5 + \sqrt{2}\].
If \[x = 2 + \sqrt{3}\] , find the value of \[x + \frac{1}{x}\].
Classify the following number as rational or irrational:
`(2sqrt7)/(7sqrt7)`
Simplify the following:
`4sqrt(28) ÷ 3sqrt(7) ÷ root(3)(7)`
Simplify the following:
`3sqrt(3) + 2sqrt(27) + 7/sqrt(3)`
Rationalise the denominator of the following:
`2/(3sqrt(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.
`4/sqrt(3)`
Simplify:
`(1/27)^((-2)/3)`
