Advertisements
Advertisements
Question
In the following determine rational numbers a and b:
`(sqrt3 - 1)/(sqrt3 + 1) = a - bsqrt3`
Advertisements
Solution
We know that rationalization factor for `sqrt3 + 1` is `sqrt3 - 1`. We will multiply numerator and denominator of the given expression `(sqrt3 - 1)/(sqrt3 + 1)` by `sqrt3 - 1` to get
`(sqrt3 - 1)/(sqrt3 + 1) xx (sqrt3 - 1)/(sqrt3 - 1) = ((sqrt3)^2 + (1)^2 - 2 xx sqrt3 xx 1)/((sqrt3)^2 - (1)^2)`
`= (3 + 1 - 2sqrt3)/(3 - 2)`
`= (4 - 2sqrt3`)/2`
`= 2 - sqrt3`
On equating rational and irrational terms, we get
`a - bsqrt3 = 2 - sqrt3`
`= 2 - 1sqrt3`
Hence we get a = 2, b = 1
APPEARS IN
RELATED QUESTIONS
Simplify the following expressions:
`(sqrt5 - sqrt3)^2`
Simplify the following expressions:
`(2sqrt5 + 3sqrt2)^2`
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`
`(2 + sqrt3)/3`
Rationales the denominator and simplify:
`(2sqrt6 - sqrt5)/(3sqrt5 - 2sqrt6)`
Simplify: \[\frac{7 + 3\sqrt{5}}{3 + \sqrt{5}} - \frac{7 - 3\sqrt{5}}{3 - \sqrt{5}}\]
If \[x = 2 + \sqrt{3}\] , find the value of \[x + \frac{1}{x}\].
Rationalise the denominator of the following:
`1/(sqrt7-sqrt6)`
Rationalise the denominator of the following:
`(3sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3))`
Simplify:
`64^(-1/3)[64^(1/3) - 64^(2/3)]`
Simplify:
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2))`
