Advertisements
Advertisements
प्रश्न
In the following determine rational numbers a and b:
`(4 + 3sqrt5)/(4 - 3sqrt5) = a + bsqrt5`
Advertisements
उत्तर
We know that rationalization factor for `4 - 3sqrt5` is `4 + 3sqrt5`. We will multiply numerator and denominator of the given expression `(4 + 3sqrt5)/(3 - 3sqrt5)` by `4 + 3sqrt5` to get
`(4 + 3sqrt5)/(4 - 3sqrt5) xx (4 + 3sqrt5)/(4 + 3sqrt5) = ((4)^2 + (3sqrt3)^2 + 2 xx 4 xx 3sqrt5)/((4)^2 - (3sqrt5)^2)`
`= (16 + 45 + 24sqrt5)/(16 - 45)`
`= (61 + 24sqrt5)/(-29)`
`= -61/29 - 24/29 sqrt5`
On equating rational and irrational terms, we get
`a + bsqrt5 = -61/29 - 24/29 sqrt5`
Hence we get `a = -61/29, b = -24/29`
APPEARS IN
संबंधित प्रश्न
Simplify the following expressions:
`(sqrt5 - 2)(sqrt3 - sqrt5)`
Find the values the following correct to three places of decimals, it being given that `sqrt2 = 1.4142`, `sqrt3 = 1.732`, `sqrt5 = 2.2360`, `sqrt6 = 2.4495` and `sqrt10 = 3.162`
`(3 - sqrt5)/(3 + 2sqrt5)`
If x= \[\sqrt{2} - 1\], then write the value of \[\frac{1}{x} . \]
If \[\frac{\sqrt{3 - 1}}{\sqrt{3} + 1}\] =\[a - b\sqrt{3}\] then
Classify the following number as rational or irrational:
2π
Simplify the following:
`sqrt(45) - 3sqrt(20) + 4sqrt(5)`
Simplify the following:
`3/sqrt(8) + 1/sqrt(2)`
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`
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))`
If `sqrt(2) = 1.414, sqrt(3) = 1.732`, then find the value of `4/(3sqrt(3) - 2sqrt(2)) + 3/(3sqrt(3) + 2sqrt(2))`.
