Question

Give that√2 is a irrational,Prove that (5+3√3) is a irrational number​

Answer 1

Step-by-step explanation:

Given that

✓2

is irrational.

We know that the theorem The product of any irrational number with a rational number is irrational.

So, since we know 3 is a rational number, 3

✓2

is irrational.

(3=

1

3

;1



=0)

Now we know that 3

2

is irrational.

Theorem: The sum of a rational number with an irrational number is irrational.

So, since we know 5 is a rational number, 5+3

2

is irrational.

(5=

1

5

;1



=0)

Thus we proved that 5+3

2

is an irrational number.

Answer 2

Answer:

First of all, please recheck before posting ur Q.

Let us assume the contrary.

i.e; 5 + 3√2 is rational

∴ 5 + 3√2 = a/b, where ‘a’ and ‘b’ are co prime integers and b ≠ 0

3√2 = a/b – 5

3√2 = a−5b/b

Or √2 = a−5b/3b

Because ‘a’ and ‘b’ are integers a−5b/3b is rational

That contradicts the fact that √2 is irrational.

The contradiction is because of the incorrect assumption that (5 + 3√2) is rational.

So, 5 + 3√2 is irrational.

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