Advertisements
Advertisements
Question
Classify the following number as rational or irrational:
2π
Solution
2π
2 is a rational number and π is an irrational number.
∵ 2π = 2 × π = Product of a rational and an irrational number is an irrational number.
∴ 2π is an irrational number.
APPEARS IN
RELATED QUESTIONS
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`
`3/sqrt10`
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)`
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`
`(1 + sqrt2)/(3 - 2sqrt2)`
Simplify `(3sqrt2 - 2sqrt3)/(3sqrt2 + 2sqrt3) + sqrt12/(sqrt3 - sqrt2)`
if `x = 2 + sqrt3`,find the value of `x^2 + 1/x^2`
\[\sqrt{10} \times \sqrt{15}\] is equal to
Rationalise the denominator of the following:
`1/(sqrt7-2)`
Simplify the following:
`3sqrt(3) + 2sqrt(27) + 7/sqrt(3)`
Rationalise the denominator of the following:
`(sqrt(3) + sqrt(2))/(sqrt(3) - sqrt(2))`