Question

show that
√3 - 2√7 is an
irrational number ?​

Answer 1

Answer:

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