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# Big Root

prove that the number 100020001 has a natural root.??

2 years, 3 months ago

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We'll be using the following identity - $x^2+2x+1=(x+1)^2$

Now, observe that

$100020001 = 10^8+2\times10^4+1 = (10^4)^2+2(10^4)+1 = (10^4+1)^2$

Thus,

$\sqrt{100020001} = 10001$ · 2 years, 3 months ago