Question

find the value of
$\sqrt{ {9999}^{2} + 19999}$
​

Answer 1

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how do i know this without using calculator :(9999²+19999)−−−−−−−−−−−−−√(9999²+19999)

elementary-number-theory square-numbers

I'm sorry to ask this question , I would like to know the value of this :(9999²+19999)−−−−−−−−−−−−−√(9999²+19999) without using calculator ?

Note :I have used digit root theory but it's not work ?

Thank you for any help

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Sep 20 '15 at 14:15

zeraoulia rafik

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Hint: 19999=2⋅9999+119999=2⋅9999+1. – Arthur Sep 20 '15 at 14:17

thank you ,Then sorry for my question, i didn't get attention – zeraoulia rafik Sep 20 '15 at 14:18

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Hint: 9999=104−19999=104−1. – Aretino Sep 20 '15 at 14:18

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99992+19999−−−−−−−−−−−√=99992+(10000−9999)(10000+9999)−−−−−−−−−−−−−−−−−−−−−−−−√=99992+(100002−99992)−−−−−−−−−−−−−−−−−−−−√=100002−−−−−−√=1000099992+19999=99992+(10000−9999)(10000+9999)=99992+(100002−99992)=100002=10000

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Sep 20 '15 at 15:42

preeti

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