Advertisements
Advertisements
Question
In the following determine rational numbers a and b:
`(3 + sqrt2)/(3 - sqrt2) = a + bsqrt2`
Advertisements
Solution
We know that rationalization factor for `3 - sqrt2` is `3 + sqrt2`. We will multiply numerator and denominator of the given expression `(3 + sqrt2)/(3 - sqrt2)` by `3 + sqrt2` to get
`(3 + sqrt2)/(3 - sqrt2) xx (3 + sqrt2)/(3 + sqrt2) = ((3)^2 + (sqrt2)^2 + 2 xx 3 sqrt2)/((3)^2 - (sqrt2)^2)`
`= (9 + 2 + 6sqrt2)/(9 - 2)`
` = (11 + 6sqrt2)/7`
`= 11/7 + 6/7 sqrt2`
On equating rational and irrational terms, we get
`a + bsqrt2 = 11/7 + 6/7 sqrt2`
Hence we get a = 11/7, b = 6/7
APPEARS IN
RELATED QUESTIONS
Rationalise the denominator of the following
`(sqrt2 + sqrt5)/3`
Simplify `(7 + 3sqrt5)/(3 + sqrt5) - (7 - 3sqrt5)/(3 - sqrt5)`
Simplify: \[\frac{3\sqrt{2} - 2\sqrt{3}}{3\sqrt{2} + 2\sqrt{3}} + \frac{\sqrt{12}}{\sqrt{3} - \sqrt{2}}\]
Write the value of \[\left( 2 + \sqrt{3} \right) \left( 2 - \sqrt{3} \right) .\]
\[\sqrt{10} \times \sqrt{15}\] is equal to
`root(4)root(3)(2^2)` equals to ______.
Rationalise the denominator of the following:
`(4sqrt(3) + 5sqrt(2))/(sqrt(48) + sqrt(18))`
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.
`4/sqrt(3)`
Simplify:
`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2))`
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.
