Home
Class 10
MATHS
Prove that 2sqrt3 is an irrational numbe...

Prove that `2sqrt3` is an irrational number

Text Solution

Verified by Experts

Rational numbers can be written in the form `p/q` where `p` and `q` are intergers and `q !=0`.
Now, given number is ,
`2sqrt3 = 2sqrt3**sqrt3/sqrt3 = 6/sqrt3`
So, it is in `p/q` form and `q !=0`.
But, as `q` is not an integer,
given number is not a rational number.
Hence, `2sqrt3` is an irrational number.
Promotional Banner

Similar Questions

Explore conceptually related problems

Prove that 2sqrt3-4 is an irrational number, using the fact that sqrt3 is an irrational number.

Prove that 2 + sqrt3 is an irrational number.

Prove that 2-3sqrt5 is an irrational number.

(i) Prove that sqrt2 is an irrational number. (ii) Prove that sqrt3 is an irrational number.

Prove that sqrt(3) is an irrational number.

Prove that sqrt(3) is an irrational number.

Prove that sqrt(3) is an irrational number.

Prove that sqrt(3) is an irrational number.

Prove that sqrt(3) is an irrational number.

Prove that 5+sqrt3 is an irrational number.