Advertisements
Advertisements
Question
Rationalise the denominator of the following:
`(2 + sqrt(3))/(2 - sqrt(3))`
Advertisements
Solution
Let `E = (2 + sqrt(3))/(2 - sqrt(3))`
For rationalising the denominator, multiplying numerator and denominator by `2 + sqrt(3)`,
`E = (2 + sqrt(3))/(2 - sqrt(3)) xx (2 + sqrt(3))/(2 + sqrt(3))`
= `(2 + sqrt(3))^2/((2)^2 - (sqrt(3)^2)`
= `(2^2 + (sqrt(3))^2 + 2 xx 2 xx sqrt(3))/(4 - 3)` ...[Using identity, (a – b)(a + b) = a2 – b2]
= `4 + 3 + 4sqrt(3)` ...[Using identity (a + b)2 = a2 + 2b + b2]
= `7 + 4sqrt(3)`
APPEARS IN
RELATED QUESTIONS
Rationalise the denominator of the following
`sqrt2/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`
`3/sqrt10`
Express the following with rational denominator:
`(sqrt3 + 1)/(2sqrt2 - sqrt3)`
Find the value of `6/(sqrt5 - sqrt3)` it being given that `sqrt3 = 1.732` and `sqrt5 = 2.236`
if `x = (sqrt3 + 1)/2` find the value of `4x^2 +2x^2 - 8x + 7`
If x= \[\sqrt{2} - 1\], then write the value of \[\frac{1}{x} . \]
Simplify \[\sqrt{3 - 2\sqrt{2}}\].
Rationalise the denominator of the following:
`(3sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3))`
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.
`1/(sqrt(3) + sqrt(2))`
Simplify:
`(1/27)^((-2)/3)`
