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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
Express the following with rational denominator:
`16/(sqrt41 - 5)`
Rationales the denominator and simplify:
`(2sqrt6 - sqrt5)/(3sqrt5 - 2sqrt6)`
Find the value of `6/(sqrt5 - sqrt3)` it being given that `sqrt3 = 1.732` and `sqrt5 = 2.236`
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`
`(3 - sqrt5)/(3 + 2sqrt5)`
Write the rationalisation factor of \[7 - 3\sqrt{5}\].
Simplify \[\sqrt{3 - 2\sqrt{2}}\].
The rationalisation factor of \[2 + \sqrt{3}\] is
Simplify the following expression:
`(sqrt5-sqrt2)(sqrt5+sqrt2)`
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))`
