A Tricky Square

$\sqrt{10000}$ = 100 x $\sqrt{10}$

$\sqrt{10000}$ = 100 X 3.162(approx)

$\sqrt{10000}$ = 316.2

Thus the required number yields its square more than 100000, thus we take the nearest integer which is $\huge{317}$

The smallest integer with its square less than $100,000$ is $316$ so the smallest integer with its square more than $100,000$ would be $316+1=\boxed{317}$

102400-639=101761; 101761-637=101124; 101124-635=100489.......... 633 is the 317th odd number.....so the answer is 317

Just take the square root of 100,000.

100√ 10

but 3<√ 10<4

So, 300<100√ 10<400

or:

316<100√ 10<400

Final answer: 317.

sqrt(100000) = 316.22 so lowest integer with square greater than 100000 is 317

\sqrt{316} < 100000 < sqrt{317}

99856 < 100000 < 100489

so, 317 is smallest number which has its square number more than 100000.