Advertisements
Advertisements
Question
Simplify the following expression:
`(sqrt5-sqrt2)(sqrt5+sqrt2)`
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
Simplify of the following:
`root(4)1250/root(4)2`
Simplify the following expressions:
`(3 + sqrt3)(5 - sqrt2)`
Simplify the following expressions:
`(11 + sqrt11)(11 - sqrt11)`
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`
`(sqrt2 - 1)/sqrt5`
In the following determine rational numbers a and b:
`(sqrt11 - sqrt7)/(sqrt11 + sqrt7) = a - bsqrt77`
Simplify: \[\frac{3\sqrt{2} - 2\sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}\]
Simplify \[\sqrt{3 + 2\sqrt{2}}\].
Simplify the following expression:
`(3+sqrt3)(3-sqrt3)`
Find the value of a and b in the following:
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = 2 - bsqrt(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.
`4/sqrt(3)`
