Advertisements
Advertisements
Question
Simplify the following expressions:
`(sqrt3 + sqrt7)^2`
Solution
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
RELATED QUESTIONS
Simplify the following expression:
`(sqrt5 - sqrt2)(sqrt5 + sqrt2)`
Simplify the following expressions:
`(2sqrt5 + 3sqrt2)^2`
Simplify
`1/(2 + sqrt3) + 2/(sqrt5 - sqrt3) + 1/(2 - sqrt5)`
In the following determine rational numbers a and b:
`(4 + 3sqrt5)/(4 - 3sqrt5) = a + bsqrt5`
Write the reciprocal of \[5 + \sqrt{2}\].
\[\sqrt{10} \times \sqrt{15}\] is equal to
Classify the following number as rational or irrational:
2π
`1/(sqrt(9) - sqrt(8))` is equal to ______.
If `sqrt(2) = 1.414, sqrt(3) = 1.732`, then find the value of `4/(3sqrt(3) - 2sqrt(2)) + 3/(3sqrt(3) + 2sqrt(2))`.
Find the value of `4/((216)^(-2/3)) + 1/((256)^(- 3/4)) + 2/((243)^(- 1/5))`
