What is the largest 5 digit perfect square?

Answer 1

316² = 99856

Answer 2

Well, let's use a technique to find the exact square that meets this requirement. We will call the five digit perfect square x.

We know that the smallest 5-digit perfect square is 100^2 (10,000). Also, we know that 400^2 (160,000) is a 6-digit perfect square.

Therefore, 100^2 < x < 400^2.

Look at 300^2 = 90,000. Replace the lower term with that.

300^2 < x < 400^2

Look at the middle point here, 350^2 = 122,500. Replace the higher term.

300^2 < x < 350^2

Continue following this method to find the largest perfect square, using the midpoint each time.

325^2 = 105,625

300^2 < x < 325^2


312^2 = 97,344

312^2 < x < 325^2


318^2 = 101,124

312^2 < x < 318^2


315^2 = 99,225

315^2 < x < 318^2


317^2 = 100,489

315^2 < x < 317^2


The number that would meet this is 316^2 = 99,856.

Answer 3

SQRT (99999) = 316.2
so 316 is the largest without producing a 6 digit number