prove that 5+3√2 is irrational
Answers
Answered by
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.
plz mark me as brainlist
Answered by
0
Answer:
it is a irrational number because√ numbers such as √3 √5 are irrational numbers...
ok.
Similar questions
Math,
4 months ago
English,
4 months ago
Hindi,
9 months ago
Computer Science,
9 months ago
Computer Science,
1 year ago
Computer Science,
1 year ago