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प्रश्न
Simplify the following expressions:
`(2sqrt5 + 3sqrt2)^2`
उत्तर
We know that `(a + b)^2 = a^2 + b^2 + 2ab`. We will use this property to simplify the expression
`(2sqrt5 + 3sqrt2)^2`
`∴ (2sqrt5 + 3sqrt2)^2 = (2sqrt5)^2 + (3sqrt2)^2 + 2 xx 2sqrt5 xx 3 sqrt2`
`= 2sqrt5 xx 2sqrt5 + 3sqrt2 xx 3sqrt2 + 2 xx 2sqrt5 xx 3sqrt2`
`= 2 xx 2sqrt(5 xx 5) + 3 xx 3sqrt(2 xx 2) + 2 xx 2 xx 3sqrt(5 xx 2)`
`= 4(5^2)^(1/2) + 9(2^2)^(1/2) + 12sqrt10`
`= 4 xx 5^1 + 9 xx 2^1 + 12sqrt10`
` = 20 + 18 + 12sqrt10`
`= 38 + 12sqrt10`
Hence the value of expression is `38 + 12sqrt10`
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संबंधित प्रश्न
Rationalise the denominator of the following
`sqrt2/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`
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Simplify:
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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.
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