Question

prove that 5-√2 is irrational.

please let me know answer quick it's urgent
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Answer 1

$\huge\underline\mathbb{\red S\pink{O}\purple{L} \blue{UT} \orange{I}\green{ON :}}$

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

$⟹5 - \sqrt{2} = \frac{a}{b}$

• [a & b are co - primes ]

$⟹5 - \frac{a}{b} = \sqrt{2}$

$⟹ \frac{5b - a}{b} = \sqrt{2}$

Since a , b and 5 are rational so their addition as well as division would be rational

But √2 is irrational and √2 cannot be equal to a rational number.

This contradicts the fact that √2 is irrational number.

This contradiction arises when we 5 - √2 as rational number.

$\underline{\boxed{\bf{\purple{∴ Therefore\;5 - \sqrt{2} \;is\;an\;irrational\;number.}}}}$

Step-by-step explanation:

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