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Prove that 5/root2 is an irrational …

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Prove that 5/root2 is an irrational no.

Posted by Ekangika Das 1 year, 2 months ago

CBSE > Class 10 > Mathematics

2 answers

Priya Rani 1 year, 2 months ago

Or Let √2 is a rational number √2 = p/q √2q= p ( square on both side ) (√2q)² = p² 2q² = p² P² is a divisible by 2q², p also divisible by 2q²( according to theorem) P = 2c ( c is a constant) P=2c ( square on both side) P² = (2c)² P² = 4c² 2q² = 4c² q² = 4c²/2 q² = 2c² q² is divisible by 2c² , then q is also divisible by 2c². In this we can see p and q have atleast one common factor : 3 Contradict the fact was p and q are co prime . proved √2 is irrational number. When we any number multiply with irrational number so answer is also irrational number. 5√2 is an irrational number. Hence proved

Priya Rani 1 year, 2 months ago

√2 is an irrational number If we add , sub, multiply, divede a number by irrational number so answer is also irrational number.

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