Question

Prove that √5 - √3 is an irrational number​

Answer 1

Step-by-step explanation:

Simple a rational number must necessarily have a rational root. Ok

(5–√−3–√)2=8−215−−√

Now 15−−√ is an irrational number since 15 is not a perfect square.

Now because irrational plus, minus, times or divided by a none-zero rational number or vice versa gives an irrational number 8−215−−√ is irrational and thus 5–√−3–√ is irrational.

This works for any expressions ab√±cd−−√ where a , b , c , d∈Q and bd isn’t a perfect square, otherwise check if a2b which is rational can equal q2∓2cqd−−√+c2d where q∈Q .

Answer 2

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