Advertisements
Advertisements
Question
Simplify the following expressions:
`(3 + sqrt3)(3 - sqrt3)`
Advertisements
Solution
We know that `(a - b)(a + b) = a^2 - b^2`. We will use this property to simplify the expression
`(3 + sqrt3)(3 - sqrt3)`
`∴ (3 + sqrt3)(3 - sqrt3) = (3)^2 - (sqrt3)^2`
`= 3^2 - sqrt3 xx sqrt3`
`= 3 xx 3 - sqrt(3 xx 3)`
`= 9 - (3^2)^(1/2)`
`= 9 - 3^1`
= 6
Hence the value of expression is 6.
APPEARS IN
RELATED QUESTIONS
Express the following with rational denominator:
`1/(2sqrt5 - sqrt3)`
Rationales the denominator and simplify:
`(2sqrt6 - sqrt5)/(3sqrt5 - 2sqrt6)`
Simplify `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + sqrt12/(sqrt3 - sqrt2)`
Simplify \[\sqrt{3 - 2\sqrt{2}}\].
The rationalisation factor of \[\sqrt{3}\] is
Simplify the following expression:
`(sqrt5+sqrt2)^2`
Simplify the following:
`root(4)(81) - 8root(3)(216) + 15root(5)(32) + sqrt(225)`
Rationalise the denominator of the following:
`16/(sqrt(41) - 5)`
Find the value of a and b in the following:
`(7 + sqrt(5))/(7 - sqrt(5)) - (7 - sqrt(5))/(7 + sqrt(5)) = a + 7/11 sqrt(5)b`
If `sqrt(2) = 1.414, sqrt(3) = 1.732`, then find the value of `4/(3sqrt(3) - 2sqrt(2)) + 3/(3sqrt(3) + 2sqrt(2))`.
