Advertisements
Advertisements
प्रश्न
In the following determine rational numbers a and b:
`(sqrt3 - 1)/(sqrt3 + 1) = a - bsqrt3`
Advertisements
उत्तर
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
संबंधित प्रश्न
Simplify of the following:
`root(4)1250/root(4)2`
Rationales the denominator and simplify:
`(1 + sqrt2)/(3 - 2sqrt2)`
Rationales the denominator and simplify:
`(2sqrt3 - sqrt5)/(2sqrt2 + 3sqrt3)`
Simplify:
`(5 + sqrt3)/(5 - sqrt3) + (5 - sqrt3)/(5 + sqrt3)`
Write the rationalisation factor of \[7 - 3\sqrt{5}\].
`1/(sqrt(9) - sqrt(8))` is equal to ______.
`root(4)root(3)(2^2)` equals to ______.
Rationalise the denominator of the following:
`sqrt(40)/sqrt(3)`
Find the value of a and b in the following:
`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = 2 - bsqrt(6)`
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.
`6/sqrt(6)`
