Math, asked by rucha515, 9 months ago

prove that 5+3√2 is irrational​

Answers

Answered by bhavna77
0

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 \sqrt{2}= \frac{p}{q}5+32=qp 

⇒ 3 \sqrt{2}= \frac{p}{q} - 532=qp−5 

⇒ 3 \sqrt{2} = \frac{p - 5q}{q}32=qp−5q 

⇒ \sqrt{2}= \frac{p-5q}{3q}2=3qp−5q 

We know that,

\sqrt{2} \ is \ irrational\ (given)2 is irrational (given) 

\frac{p-5q}{3q} \ is \ rational3qp−5q is 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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Answered by TheQuantumMan
0

Answer:

it is a irrational number because√ numbers such as √3 √5 are irrational numbers...

ok.

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