Advertisements
Advertisements
प्रश्न
In the following determine rational numbers a and b:
`(sqrt11 - sqrt7)/(sqrt11 + sqrt7) = a - bsqrt77`
Advertisements
उत्तर
We know that rationalization factor for `sqrt11 + sqrt7` is `sqrt11 - sqrt7`. We will multiply numerator and denominator of the given expression `(sqrt11 - sqrt7)/(sqrt11 + sqrt7)` by `sqrt11 - sqrt7` to get
`(sqrt11 - sqrt7)/(sqrt11 + sqrt7) xx (sqrt11 - sqrt7)/(sqrt11 - sqrt7) = ((sqrt11)^2 + (sqrt7)^2 - 2 xx sqrt11 xx sqrt7)/(sqrt(11)^2 - sqrt(7)^2)`
`= (11 + 7 - 2 sqrt77)/(11 - 7)`
`= (18 - 2sqrt77)/4`
`= 9/2 - 1/2 sqrt77`
On equating rational and irrational terms, we get
`a - bsqrt77 = 9/2 - 1/2 sqrt77`
Hence we get a = 9/2, b = 1/2
APPEARS IN
संबंधित प्रश्न
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?
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`
`(sqrt2 - 1)/sqrt5`
Write the value of \[\left( 2 + \sqrt{3} \right) \left( 2 - \sqrt{3} \right) .\]
If \[\frac{\sqrt{3 - 1}}{\sqrt{3} + 1}\] =\[a - b\sqrt{3}\] then
Simplify the following expression:
`(sqrt5+sqrt2)^2`
The number obtained on rationalising the denominator of `1/(sqrt(7) - 2)` is ______.
Rationalise the denominator of the following:
`(sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2))`
Rationalise the denominator of the following:
`(3sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3))`
Find the value of a and b in the following:
`(3 - sqrt(5))/(3 + 2sqrt(5)) = asqrt(5) - 19/11`
If `x = (sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2))` and `y = (sqrt(3) - sqrt(2))/(sqrt(3) + sqrt(2))`, then find the value of x2 + y2.
