Question

show that 4 √2 is an irracional.​

Answer 1

CORRECT QUESTION :-

★ show that 4√2 is an Irrational number.

TO PROVE :-

• 4√2 is an Irrational number.

SOLUTION :-

Rational Number :- Any number which can be expressed in the form of p/q where p and q are integers and q not equal to zero [ q ≠ 0 ].

Let, us assume that 4√2 is an rational number.So we write 4√2 as,

➠ p/q = 4√2

➠ p = 4q√2

➠ √2 = p/4q.

Here p and q are integers and not equal to zero [ q ≠ 0 ] . So from the above statement we conclude that √2 is a rational number , but we know that √2 is an "Irrational Number". Hence our assumption of 4√2 as a rational number is wrong . Hence 4√2 is an "Irrational Number.

Answer 2

Answer:

✯ Correct Question :-

• Show that 4$\sqrt{2}$ is an irrational number.

✯ To Prove :-

• 4$\sqrt{2}$ is an irrational number.

✯ Solution :-

➡ Let, us assume that 4$\sqrt{2}$ is an irrational number.

So, we can find co-prime integers "a" and"b"(b≠0) such that,

$\mapsto$ 4$\sqrt{2}$ = $\dfrac{a}{b}$

$\implies$ $\sqrt{2}$ = $\dfrac{a}{4b}$

$\therefore$ a and b are integers, $\dfrac{a}{4b}$ is a rational number and so $\sqrt{2}$ is a rational number but we know that $\sqrt{2}$ is an Irrational number.

$\therefore$ Our assumption that 4$\sqrt{2}$ is an rational number is wrong.

➣ Hence, 4$\sqrt{2}$ is an Irrational number.

$\dashrightarrow$ $\boxed{\bold{\large{PROVED}}}$

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