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Prove that √7 is irrational.

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Prove that √7 is irrational.

Posted by Ganesh Kumar Sethy 1 year, 9 months ago

CBSE > Class 10 > Mathematics

2 answers

Janhavi Singh 1 year, 9 months ago

Let assume that √7 is a rational number. So, √7=a/b (a & b are Co-prime number & b is not equal to 0) Squaring both side (√7)^2 = (a/b)^2 7 = a/b^2 7b^2 = a^2 Therefore, 7b^2 divides a^2 & a. ---------(1) Again, Let the a^2 = m^2 7m^2 = b^2 7a^2 = b^2 Therefore, 7a^2 divides b^2 & b. ---------(2) By equations (1) & (2), We get that, Our assumption is wrong. So, √7 is an Irritaional number.

Prashant Majhi 1 year, 9 months ago

√7 rrational

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