Question

Prove that 2-3 under root 7 is an irrational number

Answer 1

Answer:

We need to prove that, 2 - 3 √ 7 as Irrational number.

• We can prove such questions by contradiction method.

So, lettuce assume that 2 - 3 √ 7 as a rational number.

Hence, 2 - 3 √ 7 = p/q

By shifting,

- 3 √ 7 = p/q - 2

√ 7 = p/-3(q - 2)

Now, we observe the right-hand side as a rational number and the left-hand side as √7 that is a irrational number.

Hence, the assumption is contradicted.

Hence, it is proved that 2 - 3 √ 7 is an irrational number.

• An irrational number is a number which cannot be represented in the form of p by q where p and q are integers and q is not equal to zero.

Answer 2

2-2√3 is an irrational number

hence proved