Advertisements
Advertisements
Question
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.
`(sqrt(10) - sqrt(5))/2`
Advertisements
Solution
Let `E = (sqrt(10) - sqrt(5))/2`
= `(sqrt(5) sqrt(2) - sqrt(5))/2`
= `(sqrt(5)(sqrt(2) - 1))/2` ...`[∵ sqrt(10) = sqrt(2) sqrt(5)]`
= `(2.236(1.414 - 1))/2`
= 1.118 × 0.414
= 0.46285 ≅ 0.463
APPEARS IN
RELATED QUESTIONS
In the following determine rational numbers a and b:
`(4 + sqrt2)/(2 + sqrt2) = n - sqrtb`
Simplify `(7 + 3sqrt5)/(3 + sqrt5) - (7 - 3sqrt5)/(3 - sqrt5)`
Simplify: \[\frac{7 + 3\sqrt{5}}{3 + \sqrt{5}} - \frac{7 - 3\sqrt{5}}{3 - \sqrt{5}}\]
Write the rationalisation factor of \[\sqrt{5} - 2\].
Classify the following number as rational or irrational:
2π
Simplify the following:
`sqrt(24)/8 + sqrt(54)/9`
Simplify the following:
`root(4)(81) - 8root(3)(216) + 15root(5)(32) + sqrt(225)`
Rationalise the denominator of the following:
`16/(sqrt(41) - 5)`
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))`
Simplify:
`(256)^(-(4^((-3)/2))`
