Question

Prove that √5-√3 is not a rational number.

Answer 1

Answer:

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Step-by-step explanation:

we have to assume that √5 -√3 is a rational no which can be written in the form of p/q .

√5-√3=p/q

on squaring both the sides

(√5-√3)^2=(p/q)^2

5+3-2×√5×√3=p^2/q^2

8-2√15 = p^2q^2

now we know that 8 and -2 are rational no but √15 can not be represented in the form of p/q

hence proved .