Question

Prove that (root3+root7) is irrational​

Answer 1

Answer:

Let us suppose that √3 + √7 be a rational no.

A rational number can be written in the form of p/q where 'p' and 'q' are co-prime rational integers and q≠0.

Then, √3 + √7 = p/q.

√3=p/q-√7

squaring both sides:

3 = p²/q² + 7 - 2*p/q*√7

⇒p²/q² + 7 - 2*p/q*√7-3 = 0

⇒p²/q²+4 = 2√7-p/q

⇒

⇒

In LHS, p and q are already taken as rational integers, 2 & 4 are also rational, and denominator ≠0. So, the LHS is rational. But we know that √7 is irrational. So, this contradicts us.

Thus proved that √3+√7 is irrational.

Answer 2

Answer:

yes

Step-by-step explanation:

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