Question

Prove tha 3\√5 is irrational?

Answer 1

Answer:

i dont know

Step-by-step explanation:

d

Answer 2

Answer:

Let us assume 3√5 is a rational number.

3√5 = a/b (where b≠0)

3 = a/b-√5

Squaring on both sides...

(3)² = [a/b-√5]²

9 = [a²/b²+(√5)²-2(a/b) (√5)

[Since (a-b) ²= a²+b²-2ab]

Rearranging.....

2a/b√5 = a²/b²+25-9

2a/b √5 = a²/b² +16

2a/b √5 = a²+16b²/b²

√5 = a²+16b²/b²×b/2a

√5 = a²+16b²/2ab

Here L. H. S = √5 = irrational number.

R. H. S = a²+16b²/2ab = rational number.

An irrational number is not equal to rational number. This contradicts the fact.

So, our assumption is wrong that 3√5 is a rational number.

:. 3√5 is an irrational number.....

Hence proved.

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