Advertisements
Advertisements
Question
In the following determine rational numbers a and b:
`(sqrt3 - 1)/(sqrt3 + 1) = a - bsqrt3`
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
Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π = `c/d`. This seems to contradict the fact that π is irrational. How will you resolve this contradiction?
Simplify the following expressions:
`(4 + sqrt7)(3 + sqrt2)`
Simplify the following expressions:
`(3 + sqrt3)(5 - sqrt2)`
Express the following with rational denominator:
`1/(3 + sqrt2)`
If \[a = \sqrt{2} + 1\],then find the value of \[a - \frac{1}{a}\].
If \[\frac{\sqrt{3 - 1}}{\sqrt{3} + 1}\] =\[a - b\sqrt{3}\] then
Classify the following number as rational or irrational:
`(2sqrt7)/(7sqrt7)`
Simplify the following expression:
`(sqrt5+sqrt2)^2`
The number obtained on rationalising the denominator of `1/(sqrt(7) - 2)` is ______.
Value of (256)0.16 × (256)0.09 is ______.
