Advertisements
Advertisements
Question
Examine, whether the following number are rational or irrational:
`(2-sqrt2)(2+sqrt2)`
Solution
Let `x=(2-sqrt2)(2+sqrt2)`
`rArrx=(2)^2-(sqrt2)^2` {As (a + b)(a - b) = a2 - b2}
⇒ x = 4 - 2
⇒ x = 2
So `(2-sqrt2)(2+sqrt2)` is a rational number
APPEARS IN
RELATED QUESTIONS
Define an irrational number ?
Give an example of two irrational numbers whose:
quotient is an irrational number.
Give an example of two irrationals whose sum is rational.
Prove that `(2+sqrt3)/5` is an irrational number, given that `sqrt 3` is an irrational number.
Check whether the square of the following is rational or irrational:
`3 + sqrt(2)`
Represent the number `sqrt(7)` on the number line.
Number of rational numbers between 15 and 18 is finite.
Classify the following number as rational or irrational with justification:
`(1 + sqrt(5)) - (4 + sqrt(5))`
Insert a rational number and an irrational number between the following:
2 and 3
Given that `sqrt(3)` is irrational, prove that `5 + 2sqrt(3)` is irrational.
