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Prove underroot 3+underroot 5 is irrational |
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Answer» Answer to prove se start hai unlock 35 lakh questionsWhat\'s your doubt?10th>Maths>Real Numbers>Revisiting Irrational Numbers>Prove that √(3) + √(5) is...MathsBookmarkProve that 3\u200b + 5\u200b is irrational.EasyshareShareAnswerTo prove : 3\u200b + 5\u200b is irrational.Let us assume it to be a rational number. Rational numbers are the ones that can be expressed in qp\u200b form where p,q are integers and q isn\'t equal to zero.3\u200b + 5\u200b = qp\u200b 3\u200b = qp\u200b − 5\u200b squaring on both sides, 3= q 2 p 2 \u200b −2. 5\u200b ( qp\u200b )+5⇒ q(2 5\u200b p)\u200b =5−3+( q 2 p 2 \u200b ) ⇒ q(2 5\u200b p)\u200b = q 2 2q 2 −p 2 \u200b ⇒ 5\u200b = q 2 2q 2 −p 2 \u200b . 2pq\u200b ⇒ 5\u200b = 2pq(2q 2 −p 2 )\u200b As p and q are integers RHS is also rational.As RHS is rational LHS is also rational i.e 5\u200b is rational.But this contradicts the fact that 5\u200b is irrational.This contradiction arose because of our false assumption.so, 3\u200b + 5\u200b irrational. |
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