Advertisements
Advertisements
Question
Simplify the following expression:
`(sqrt5 - sqrt2)(sqrt5 + sqrt2)`
Advertisements
Solution
The given expression is `(sqrt5 - sqrt2) (sqrt5 + sqrt2)`
We know that (a + b) (a - b) = a2 - b2
⇒ `(sqrt5 - sqrt2) (sqrt5 + sqrt2) = (sqrt5)^2 - (sqrt2)^2`
⇒ `(sqrt5 - sqrt2) (sqrt5 + sqrt2) = 5 - 2`
∴ `(sqrt5 - sqrt2) (sqrt5 + sqrt2) = 3`
APPEARS IN
RELATED QUESTIONS
Classify the following numbers as rational or irrational:
`2-sqrt5`
Simplify the following expressions:
`(sqrt3 + sqrt7)^2`
Rationalise the denominator of the following
`(3sqrt2)/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`
`(sqrt5 + 1)/sqrt2`
Find the value of `6/(sqrt5 - sqrt3)` it being given that `sqrt3 = 1.732` and `sqrt5 = 2.236`
Simplify \[\sqrt{3 - 2\sqrt{2}}\].
Simplify the following:
`sqrt(45) - 3sqrt(20) + 4sqrt(5)`
Rationalise the denominator of the following:
`(2 + sqrt(3))/(2 - sqrt(3))`
Rationalise the denominator of the following:
`(4sqrt(3) + 5sqrt(2))/(sqrt(48) + sqrt(18))`
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.
`6/sqrt(6)`
