Question

Prove that 3-2√7 is irrational number

Answer 1

Given: The term 3-2√7.

To find: Prove that 3 - 2√7 is an irrational number.

Solution:

• Now we have given the term: 3 - 2√7

• Consider 3 - 2√7 as a rational number, then we can write it in the form of a/b, where a and b are co prime.

                 3 - 2√7 = a/b

                 -2√7 = a/b - 3

                 -2√7 = (a-3b)/b

                 √7 = (-a+3b)/2b

• So this proves that (3b - a)/2b is a rational number.

• But √7 is an irrational number so it contradicts our assumption.

• So our assumption is wrong.

                 3 - 2√7 is an irrational number.

Answer:

               So 3 - 2√7 is an irrational number.

Answer 2

Answer:

Now we have given the term: 3 - 2√7

Consider 3 - 2√7 as a rational number, then we can write it in the form of a/b, where a and b are co prime.

                3 - 2√7 = a/b

                -2√7 = a/b - 3

                -2√7 = (a-3b)/b

                √7 = (-a+3b)/2b

So this proves that (3b - a)/2b is a rational number.

But √7 is an irrational number so it contradicts our assumption.

So our assumption is wrong.

                3 - 2√7 is an irrational number.

Step-by-step explanation: