Given thatal is irrational, prove that (5 32) is an irrational number

1.	Given thatal is irrational, prove that (5 32) is an irrational number
Answer» Given that,√2 is irrational To prove:5 + 3√2 is irrational Assumption:Let us assume 5 + 3√2 is rational. Proof:As 5 + 3√2 is rational. (Assumed) They must be in the form of p/q where q≠0, and p & q are co prime. Then,⇒ 5+3√2 = p/q⇒3√2 = p/q - 5⇒√2 = (p-5q)/3q We know that,√2 is irrational (given) (p - 5q)/3q = rational And, Rational≠ Irrational. Therefore we contradict the statement that, 5+3√2 is rational. Hence proved that 5 + 3√2 is irrational.

Answer»

Given that,√2 is irrational

To prove:5 + 3√2 is irrational

Assumption:Let us assume 5 + 3√2 is rational.

Proof:As 5 + 3√2 is rational. (Assumed) They must be in the form of p/q where q≠0, and p & q are co prime.

Then,⇒ 5+3√2 = p/q⇒3√2 = p/q - 5⇒√2 = (p-5q)/3q

We know that,√2 is irrational (given) (p - 5q)/3q = rational

And, Rational≠ Irrational.

Therefore we contradict the statement that, 5+3√2 is rational.

Hence proved that 5 + 3√2 is irrational.

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