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Prove that 2 is an irrational …

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Prove that 2 is an irrational number

Posted by Mohammad Dawood 6 years, 5 months ago

CBSE > Class 10 > Mathematics

2 answers

Shruti Jha 6 years, 5 months ago

Let root 3 is rational number. root3 =p/q ( where, p and q are integer , q is not equal to 0 and p and q are co-primes ). root 3q = p. Squaring both sides. 3p2=q2 (q square and p square)...... (i). 3 divides p2. 3 divides p.......... (ii). p2 = 3q2. p2 =3m. Put the value of p2. p2=3q2. (3m)2=3q2. 9m2=3q2. 3m2=q2. q2=3m2. 3 divides q2. 3 divides q.......... (iii). By eqn (ii) and (iii) 3 divides p and 3 divides also q. 3 is the common factor of p and q. This is contradiction because our assumption is wrong. Hence, root 3 is irrational number.

2Thank You

Shruti Jha 6 years, 5 months ago

2 or root 2

2Thank You

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CBSE > Class 10 > Mathematics