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प्रश्न
Simplify \[\sqrt{3 - 2\sqrt{2}}\].
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उत्तर
We are asked to simplify`sqrt(3 - 2sqrt2)` It can be written in the form `(a-b)^2 = a^2 +b^2 - 2ab ` as
`sqrt(3-2sqrt2) = sqrt(2 +1 - 2 xx 1 xx sqrt2)`
` = sqrt((sqrt2)^2 + (1)^2 - 2xx 1xxsqrt2)`
` = sqrt((sqrt2 - 1)^2)`
` = sqrt2 - 1`
Hence the value of the given expression is`sqrt2 - 1`.
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संबंधित प्रश्न
Simplify the following expressions:
`(2sqrt5 + 3sqrt2)^2`
Rationalise the denominator of the following
`(sqrt2 + sqrt5)/3`
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`16/(sqrt41 - 5)`
In the following determine rational numbers a and b:
`(3 + sqrt2)/(3 - sqrt2) = a + bsqrt2`
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)`
Write the reciprocal of \[5 + \sqrt{2}\].
If\[\frac{\sqrt{3} - 1}{\sqrt{3} + 1} = x + y\sqrt{3},\] find the values of x and y.
Rationalise the denominator of the following:
`(3 + sqrt(2))/(4sqrt(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(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.
`1/(sqrt(3) + sqrt(2))`
