Question

(b) 5 + 3√2 is an irrational number. PROVE THAT

Answer 1

$\large\bf\underline {To \: prove:-}$

• 5 +3√2 is irrational

$\huge\bf\underline{Solution:-}$

Let us assume,that 5+3√2 is rational.

Then,

$: \implies \rm \:5 + 3 \sqrt{2} = \frac{a}{b}$

where a and b are co-primes and b ≠0

$: \implies \rm \:5 + 3 \sqrt{2} = \frac{a}{b} \\ \\ : \implies \rm \:3 \sqrt{2} = \frac{a}{b} - 5 \\ \\ : \implies \rm \:3 \sqrt{2} = \frac{a - 5b}{b} \\ \\ : \implies \rm \: \sqrt{2} = \frac{a - 5b}{3b}$

Since , $\frac{a - 5b}{3b}$ is in the form of p/q so, $\frac{a - 5b}{3b}$ is rational.

Then , √2 is also rational .

But we know that√2 is irrational.

So, this contradiction is arissen because of our wrong assumption.

hence, Proved that 5 +3√2 is irrational

Answer 2

Answer:

yes it is irrational number