Show that√3 - 2√7 is anirrational number ?

1.	Show that√3 - 2√7 is anirrational number ?
Answer» 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

Answer»

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

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Show that√3 - 2√7 is anirrational number ?​

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Show that√3 - 2√7 is anirrational number ?