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प्रश्न
Simplify the following expressions:
`(4 + sqrt7)(3 + sqrt2)`
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उत्तर
We can simplify the expression `(4 + sqrt7)(3 + sqrt2)` as
`(4 + sqrt7)(3 + sqrt2) = 4 xx 3 + 4 xx sqrt2 + 3 xx sqrt7 + sqrt7 xx sqrt2 `
`= 12 + 4sqrt2 + 3sqrt7 + sqrt(7xx2)`
`= 12 + 4sqrt2 + 3sqrt7 + sqrt14`
Hence the value of the expression is `12 + 4sqrt2 + 3sqrt7 + sqrt14`
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संबंधित प्रश्न
Simplify the following expressions:
`(sqrt5 - 2)(sqrt3 - sqrt5)`
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`
`
Simplify: \[\frac{3\sqrt{2} - 2\sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}\]
If \[x = 2 + \sqrt{3}\] , find the value of \[x + \frac{1}{x}\].
Simplify the following expression:
`(sqrt5-sqrt2)(sqrt5+sqrt2)`
Rationalise the denominator of the following:
`16/(sqrt(41) - 5)`
Rationalise the denominator of the following:
`(sqrt(3) + sqrt(2))/(sqrt(3) - 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.
`(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))`
If `sqrt(2) = 1.414, sqrt(3) = 1.732`, then find the value of `4/(3sqrt(3) - 2sqrt(2)) + 3/(3sqrt(3) + 2sqrt(2))`.
