Question

show that show that 6 + root 2 is irrational
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Answer 1

Answer:

yes,6+root2 is a irrational number.

Step-by-step explanation:

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Answer 2

Let assume that 6+√2 is not an irrational number, but a rational number.

$∴ \blue{\: If \: 6 +\sqrt{2} \: is \:a \: rational \: then, }\\\blue{ 6 + \sqrt{2} =\frac{p}{q}}$

$∴ </strong><strong>\</strong><strong>blue</strong><strong>{</strong><strong>\: We \: get \: \sqrt{3} = \frac{p}{q}</strong><strong> - 6</strong><strong>}</strong><strong>\</strong><strong>\</strong><strong>$

In this equation left side is an irrational number and right side is a rational number which is an contradictory so

6 + √2 is not a rational number but an irrational number. Hence, proved.