Advertisements
Advertisements
Question
Simplify the following expressions:
`(sqrt5 - sqrt3)^2`
Solution
We know that `(a - b)^2 = a^2 + b^2 - 2ab`. We will use this property to simplify the expression
`(sqrt5 - sqrt3)`
`∴ (sqrt5 - sqrt3)^2 = (sqrt5)^2 + (sqrt3)^2 - 2 xx sqrt5 xx sqrt3`
`= sqrt5 xx sqrt5 + sqrt3 xx sqrt3 - 2 xx sqrt(5 xx 3)`
`= sqrt(5 xx 5) + sqrt(3 xx 3) - 2 xx sqrt(5 xx 3)`
`= (5^2)^(1/2) + (3^2)^(1/2) - 2sqrt15`
`= 5^1 + 3^1 - 2sqrt15`
`= 8 - 2sqrt15`
Hence the value of expression is `8 - 2sqrt15`
APPEARS IN
RELATED QUESTIONS
Simplify of the following:
`root(4)1250/root(4)2`
Rationalise the denominator of each of the following
`1/sqrt12`
Rationales the denominator and simplify:
`(5 + 2sqrt3)/(7 + 4sqrt3)`
Simplify `(7 + 3sqrt5)/(3 + sqrt5) - (7 - 3sqrt5)/(3 - sqrt5)`
Simplify: \[\frac{7 + 3\sqrt{5}}{3 + \sqrt{5}} - \frac{7 - 3\sqrt{5}}{3 - \sqrt{5}}\]
If \[\frac{\sqrt{3 - 1}}{\sqrt{3} + 1}\] =\[a - b\sqrt{3}\] then
Simplify the following expression:
`(sqrt5+sqrt2)^2`
Simplify the following:
`sqrt(24)/8 + sqrt(54)/9`
Rationalise the denominator of the following:
`2/(3sqrt(3)`
Simplify:
`(256)^(-(4^((-3)/2))`
