Advertisements
Advertisements
प्रश्न
Prove that of the numbers `2 + sqrt (5)` is irrational:
उत्तर
Let `2 + sqrt (5)` be rational.
Hence, `2 + sqrt (5)` and `sqrt( 5 )` are rational.
∴ `(2 + sqrt (5))` – 2 = `2 + sqrt (5)`– `2 = sqrt (5)` = rational [∵Difference of two rational is rational]
This contradicts the fact that `sqrt (5)` is irrational.
The contradiction arises by assuming `2 - sqrt (5)` is rational.
Hence, `2 - sqrt (5)` is irrational.
APPEARS IN
संबंधित प्रश्न
Given that `sqrt2` is irrational prove that `(5 + 3sqrt2)` is an irrational number
Examine, whether the following number are rational or irrational:
`(sqrt2-2)^2`
Prove that of the numbers `5 + 3 sqrt (2)` is irrational:
Prove that 5`sqrt(2)` is irrational.
Give an example of two irrationals whose sum is rational.
Which of the following is irrational?
Which of the following is irrational?
Find the square of : √5 - 2
State whether the following number is rational or irrational
`(3 + sqrt(3))^2`
Classify the following number as rational or irrational with justification:
0.5918
