Is 1,000 a Perfect Square?

No, 1,000 is not a perfect square.

Quick math

  • √1,000 ≈ 31.6228
  • 312 = 961 < 1,000 < 1,024 = 322
  • 1,000 = 23 × 53
Perfect square
No
Square root
≈ 31.6228
Simplest radical form
10√10
Prime factorization
2³ × 5³
Try your own numbers

Is 1,000 a Perfect Square?

No, 1,000 is not a perfect square. It lies between 31² = 961 and 32² = 1,024.

Handwritten notebook page checking whether 1,000 is a perfect square
1,000 lies between two consecutive perfect squares, so it is not a perfect square.

Step 1: The Square Root of 1,000

√1,000 ≈ 31.6228. The root is not a whole number, so the number is not a perfect square.

Step 2: Prime Factorization

1,000 = 2³ × 5³. At least one exponent is odd, so the number cannot be a perfect square.

Step 3: Simplest Radical Form

√1,000 = 10√10. Pull the square factors out of the root: 10² comes out as 10.

Try another number

Check any other number in the Perfect Square Calculator.

More Perfect Square Calculator Examples

Is 1,000 a Perfect Square?: FAQs

Is 1,000 a perfect square?

No. No whole number multiplied by itself gives 1,000. It sits between 31² = 961 and 32² = 1,024.

What is the square root of 1,000?

The square root of 1,000 is about 31.6228, which simplifies to 10√10.

How do you check if 1,000 is a perfect square using prime factors?

Write 1,000 as 2³ × 5³. The exponent of 2, 5 is odd, so the primes cannot all be paired and 1,000 is not a perfect square.

What is the next perfect square after 1,000?

The next perfect square after 1,000 is 32² = 1,024.

More Worked Examples

Showing 4 of 4 examples