Advertisements
Advertisements
Question
Simplify the following expressions:
`(2sqrt5 + 3sqrt2)^2`
Advertisements
Solution
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`
APPEARS IN
RELATED QUESTIONS
Simplify the following expression:
`(sqrt5 - sqrt2)(sqrt5 + sqrt2)`
Rationalise the denominator of the following
`(sqrt3 + 1)/sqrt2`
Rationales the denominator and simplify:
`(2sqrt6 - sqrt5)/(3sqrt5 - 2sqrt6)`
Rationales the denominator and simplify:
`(2sqrt3 - sqrt5)/(2sqrt2 + 3sqrt3)`
The rationalisation factor of \[\sqrt{3}\] is
Rationalise the denominator of the following:
`sqrt(6)/(sqrt(2) + sqrt(3))`
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)`
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)`
If `x = (sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2))` and `y = (sqrt(3) - sqrt(2))/(sqrt(3) + sqrt(2))`, then find the value of x2 + y2.
Simplify:
`(256)^(-(4^((-3)/2))`
