Question

Prove that 7+3√2 is not a rational number

Answer 1

QUESTION:

Prove that 7+3√2 is not a rational number

ANSWER:

Let;

$7 + 3 \sqrt{2}$

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

so,

$7 + 3 \sqrt{2} = \frac{a}{b} \\ \frac{a}{b} - 7 \\ 3 \sqrt{2} = \frac{7a - b}{7} \\ \sqrt{2} = \frac{7a - b}{7} \div 3 \\ \sqrt{2 } = \frac{7a - b}{21}$

hence, here contradiction arises as we know that root 2 is a irrational number.

Hence, proved.

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