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प्रश्न
Simplify the following expressions:
`(4 + sqrt7)(3 + sqrt2)`
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
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`
`(2 + sqrt3)/3`
In the following determine rational numbers a and b:
`(3 + sqrt2)/(3 - sqrt2) = a + bsqrt2`
Write the value of \[\left( 2 + \sqrt{3} \right) \left( 2 - \sqrt{3} \right) .\]
Simplify \[\sqrt{3 - 2\sqrt{2}}\].
Rationalise the denominator of the following:
`1/(sqrt7-2)`
The value of `(sqrt(32) + sqrt(48))/(sqrt(8) + sqrt(12))` is equal to ______.
Value of (256)0.16 × (256)0.09 is ______.
Rationalise the denominator of the following:
`16/(sqrt(41) - 5)`
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)`
