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Number Theory Level 4

How many whole numbers that are perfect squares can be displayed on a 15 15 - digit calculator?


The answer is 31622777.

Mardokay Mosazghi by Mardokay Mosazghi , 22, USA

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3 solutions

Saket Sharma
Sep 20, 2014

[ 1 0 15 ] + 1 [\sqrt{10^{15}}] + 1 , where [ N ] [N] represents greatest integer less than N. 1 is added to include 0, as question asks for whole numbers.

Now, [ 1 0 15 ] = [ 1 0 7 . 10 ] = 31622776 [\sqrt{10^{15}}] = [10^{7}.\sqrt{10}] = 31622776

Therefore, answer = 31622776 + 1 = 31622777 = 31622776 + 1 = 31622777

3 Helpful 0 Interesting 0 Brilliant 0 Confused

but the above formula does not yield answer to 5 digit !!

sai krishna - 6 years, 4 months ago
Shahzaib Zaman
Nov 25, 2014

999999999999999^1/2 +1

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Suhaas Shukla
Sep 10, 2014

(999999999999999)^1/2 + 1

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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