√5 अपरिमेय संख्या है

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√5 अपरिमेय संख्या है

Posted by Edit Kb 1 year, 2 months ago

CBSE > Class 10 > गणित

1 answers

Srishty Kumari 1 year, 2 months ago

Let us assume √5 is rational number which can be written in the form p/q there for √5=p/q (where p and q are co-prime integer and q is not equal to 0) √5q=p --equation first squareing both side 5q²=p² here five divides p² Therefore 5 also divides p let p = 5C putting value of p is equation first equation √5q= 5C squaring both side 5q² = 25c² q²=5c² q²/5 =c² Here 5 divides q² Therefore 5 also divides q Here we can see 5 divides both integer p and q but it contradicts that p and q are co prime integer this contradiction arising due to our wrong assumption therefore √ 5 is irrational number.

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