What is a square root of 80?

Understanding the Square Root of 80

When you ask what the square root of 80 is, the answer isn’t a whole number—but it’s close to one. The square root of 80 is approximately 8.944. This means that when you multiply 8.944 by itself, you get a number very close to 80.

To be precise: 8.944 × 8.944 ≈ 79.99, which rounds up to 80. It’s not exact because √80 is an irrational number—its decimal representation goes on forever without repeating. So, we usually round it to a few decimal places for simplicity.

You might wonder why we can’t just say the square root is a neat number like 9. After all, 9² = 81, which is close. But 80 isn’t a perfect square, so we need to dig a little deeper. One way to estimate the square root is through a method called "long division" or successive approximation—essentially narrowing in on the correct value step by step.

Another helpful trick is to simplify √80 using factors. Since 80 = 16 × 5 and √16 = 4, we can write √80 as 4√5. Knowing that √5 ≈ 2.236, multiplying 4 × 2.236 also gives us about 8.944. This algebraic shortcut is often useful in math problems where exact form matters more than decimal precision.

Whether you're solving equations, working on geometry, or just curious about numbers, understanding how to break down and approximate square roots like √80 makes math more approachable. So next time you see 80 under a radical, remember—it’s not mysterious, just irrational.