Advertisements
Advertisements
Question
Prove that of the numbers ` 2 - sqrt(3)` is irrational:
Solution
Let 2 - `sqrt (3)` be rational.
Hence, 2 and 2 - `sqrt (3)` are rational.
∴ (2 - 2 + `sqrt (3)` ) = `sqrt (3)` = rational [∵ Difference of two rational is rational]
This contradicts the fact that `sqrt (3)` is irrational.
The contradiction arises by assuming 2 - `sqrt (3)` is rational.
Hence, 2 - `sqrt (3)` is irrational.
APPEARS IN
RELATED QUESTIONS
In the following equation, find which variables x, y, z etc. represent rational or irrational number:
v2 = 3
Prove that the following number is irrational: √3 + √2
Prove that the following number is irrational: 3 - √2
Check whether the square of the following is rational or irrational:
`3 + sqrt(2)`
Write a pair of irrational numbers whose sum is rational.
The product of a rational and irrational number is ______.
The product of two different irrational numbers is always ______.
Find three rational numbers between `5/7` and `6/7`
Insert a rational number and an irrational number between the following:
0 and 0.1
Prove that `3 - 2sqrt(5)` is an irrational number, given that `sqrt(5)` is an irrational number.
