Advertisements
Advertisements
प्रश्न
Simplify the following expressions:
`(sqrt3 + sqrt7)^2`
Advertisements
उत्तर
We know that `(a + b)^2 = a^2 + b^ + 2ab` We will use this property to simplify the expression
`(sqrt3 + sqrt7)^2`
`∴(sqrt3 + sqrt7)^2 = (sqrt3)^2 + (sqrt7)^2 + 2 xx sqrt3 xx sqrt7`
`= sqrt(3 xx 3) + sqrt(7 xx 7) + 2 xx sqrt(3 xx 7)`
`= (3^2)^(1/2) + (7^2)^(1/2) + 2sqrt21`
`= 3^1+ 7^1 + 2sqrt21`
`= 10 + 2sqrt21`
Hence the value of expression is `10 + 2sqrt21`
APPEARS IN
संबंधित प्रश्न
Simplify the following expressions:
`(3 + sqrt3)(5 - sqrt2)`
Rationalise the denominator of the following
`sqrt2/sqrt5`
Rationales the denominator and simplify:
`(3 - sqrt2)/(3 + sqrt2)`
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`
`(1 + sqrt2)/(3 - 2sqrt2)`
Write the reciprocal of \[5 + \sqrt{2}\].
Rationalise the denominator of the following:
`1/(sqrt7-2)`
Simplify the following:
`sqrt(24)/8 + sqrt(54)/9`
Simplify the following:
`(2sqrt(3))/3 - sqrt(3)/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)`
