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प्रश्न
Simplify the following expressions:
`(11 + sqrt11)(11 - sqrt11)`
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उत्तर
We know that `(a + b)(a - b) = a^2 - b^2` We will use this property to simplify the expression
`(11 + sqrt11)(11 - sqrt11)`
`∴ (11 + sqrt11)(11 - sqrt11) = 11^2 - (sqrt11)^2`
`= 11 xx 11 - sqrt11 xx sqrt11`
`= 121 - sqrt(11 xx 11)`
`= 121 - (11^2)^(1/2)`
= 121 - 11
= 110
Hence the value of expression is 110.
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संबंधित प्रश्न
Classify the following numbers as rational or irrational:
`2-sqrt5`
Rationalise the denominator of each of the following
`1/sqrt12`
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`
`(sqrt10 + sqrt15)/sqrt2`
`
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`
If \[\frac{\sqrt{3 - 1}}{\sqrt{3} + 1}\] =\[a - b\sqrt{3}\] then
Rationalise the denominator of the following:
`1/(sqrt5+sqrt2)`
Simplify the following:
`sqrt(24)/8 + sqrt(54)/9`
Find the value of a and b in the following:
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = 2 - bsqrt(6)`
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)`
Simplify:
`(256)^(-(4^((-3)/2))`
