Question

classify 5-3√5 as rational or irrational​

Answer 1

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5 - 3√5 is an irrational number

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Answer 2

We know, $\sqrt{5}$ is an irrational number.

So, $3\sqrt{5}$ is also an irrational number.

Proof:

Let $3\sqrt{5}$ be a rational number.

$3\sqrt{5} = \dfrac{a}{b}$

where a and b are integers, $b\neq 0$ and a and b are co-prime numbers.

$\sqrt{5} = \dfrac{a}{3b}$

This contradicts the fact.

Hence $3\sqrt{5}$ is an irrational number.

☆ We know, subtraction of rational number (here, 5) and irrational number(here, $\bold{3\sqrt{5} = \dfrac{a}{b}}$) always gives irrational number.

Therefore,

$5-3\sqrt{5}$ is classified as irrational.