Question

Show that 5-3√2 is irrational.

Answer 1

Step-by-step explanation:

Aloha !

.

Let us assume that 5-3√2 is rational number.

Now ,

5-3√2=p/q

-3√2=-5+(p/q)

3√2=5-(p/q)

3√2=5q-p/q

√2=5q-p/3q

RHS is rational . Such that LHS should be a rational number.

Therefore 5-3√2 is irrational.

Thank you

@ Twilight Astro ✌️☺️♥️

Answer 2

Step-by-step explanation:

TO PROVE THAT 5-3/2 IS IRRATIONAL.

LET

$5 - 3 \sqrt{2}$

is a rational number in the form of a by b.

so

$5 - 3 \sqrt{2} = \frac{a}{b} \\ \\ - 3 \sqrt{2} = \frac{a}{b} - 5 \\ \\ - 3 \sqrt{2} = \frac{a - 5b}{b} \\ \\ \sqrt{2 } = \frac{a - 5b}{ - 3b}$

HENCE HERE CONTRADICTION ARISES AS WE KNOW THAT

$\sqrt{2}$

is an irrational number.

HENCE PROVED! !!!!!!!!