Square Roots From 1 to 25: Complete Chart With Examples (2026 Guide)

You’re staring at a math problem, and there it is that little checkmark symbol sitting over a number, silently asking “what times itself gives you this?” That’s a square root, and honestly, once it clicks, it’s one of the easier concepts in math. The tricky part is usually just getting a clear reference and a bit of practice. This guide is exactly that a full square roots chart from 1 to 25, explained the way I’d walk a student through it in person, not the way a textbook drones on about it.

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What Is a Square Root, Really?

Think of it as squaring in reverse. If you square a number, you multiply it by itself. A square root asks the opposite question: what number, multiplied by itself, gets you back to where you started? So: 5 × 5 = 25 means the square root of 25 is 5. Written out, that’s √25 = 5. The little checkmark is called a radical sign, and whatever number sits under it is the radicand though honestly, you don’t need to remember that word to use the concept.

Perfect Squares vs. Everything Else

Here’s where a lot of the confusion starts, so let’s sort it out early. Perfect squares are numbers that come from squaring a whole number so their square roots are also nice, clean whole numbers. 1, 4, 9, 16, and 25 are your perfect squares between 1 and 25. Everything else? Their square roots are messier, decimals that never actually end or repeat in a clean pattern. We just round them to a few decimal places and move on, which is totally fine for practical use.

The Full Chart: Square Roots From 1 to 25

Here’s the complete list. Non-perfect squares are rounded to three decimal places, which is more than enough precision for schoolwork or everyday calculations.

Number (n) Square (n²) Square Root (√n)

1 1 1.000

2 4 1.414

3 9 1.732

4 16 2.000

5 25 2.236

6 36 2.449

7 49 2.646

8 64 2.828

9 81 3.000

10 100 3.162

11 121 3.317

12 144 3.464

13 169 3.606

14 196 3.742

15 225 3.873

16 256 4.000

17 289 4.123

18 324 4.243

19 361 4.359

20 400 4.472

21 441 4.583

22 484 4.690

23 529 4.796

24 576 4.899

25 625 5.000

Worth noticing: the “Square” column is basically a squares chart hiding inside a square roots chart. If you’re studying both topics together (which, let’s be honest, you probably are), this one table covers you for both.

The Five Perfect Squares Worth Actually Memorizing

Out of all 25 numbers, only five give you a clean whole-number root. These five are worth burning into memory because they show up everywhere algebra, geometry, random word problems:

√1 = 1
√4 = 2
√9 = 3
√16 = 4
√25 = 5

Get comfortable with just these five, and you’ve got anchor points that make every other square root in this range much easier to estimate. More on that in a second.

How People Actually Calculate Square Roots

Prime Factorization – Great for Perfect Squares

This one’s clean and satisfying when it works.

Finding √16:

1. Break 16 down into primes: 2 × 2 × 2 × 2

2. Pair up the matching factors: (2×2) × (2×2)

3. Pull one number out of each pair: 2 × 2 = 4 4. So √16 =4

Finding √144:

1. Prime factors: 2 × 2 × 2 × 2 × 3 × 3

2. Pair them up: (2×2) × (2×2) × (3×3)

3. Pull one from each: 2 × 2 × 3 = 12

4. So √144 = 12

Estimation – Your Best Friend for Everything Else

Most numbers aren’t perfect squares, so this is the method you’ll actually reach for most often.

Estimating √20:

What perfect squares sit around 20? That’s 16 and 25.

2. 20 sits closer to 16 than to 25, so the answer should land closer to 4 than to 5.

3. Try 4.4 → 4.4 × 4.4 = 19.36 (a little low). Try 4.5 → 4.5 × 4.5 = 20.25 (a little high).

4. So √20 lands around 4.47 — matches the chart above.

Long Division Method - For When You Need Precision By Hand

Schools still teach this one for a reason, it gets you an exact decimal answer without any tech. It’s a bit more involved than the two methods above, so it’s really only worth pulling out when a calculator isn’t allowed and you need real precision. Happy to walk through a full worked example separately if that’s useful to you.

Just Using a Calculator

And sometimes, honestly, you just tap it into your phone. There’s nothing wrong with that for everyday situations but knowing the manual methods above means you’ll actually notice if you fatfingered a number and the answer looks off.

Where Square Roots Sneak Into Real Life

It’s easy to assume this stuff disappears the moment you leave the classroom, but it really doesn’t:

Home renovation: A square room with 225 square feet of floor space? Each side is √225 = 15 feet.
Design work: Diagonal measurements and aspect ratios lean on square roots more than you’d think.
Finance: Standard deviation, a core concept in investment risk is calculated using square roots.
Construction: The Pythagorean theorem (a² + b² = c²) needs square roots to find a diagonal length, which is how builders check that a structure is properly squared up.
Sports stats: Even performancevariance calculations for athletes lean on the same math.

Tricks That Actually Help You Remember These Faster

Lock in the five perfect squares first. They’re your reference points for everything else.
Lean on the “nearest perfect square” trick when estimating, it works surprisingly well.
Notice the pattern in the differences. Going from one perfect square to the next, the gap grows by 2 each time (1, 4, 9, 16, 25 → gaps of 3, 5, 7, 9). Once you see this pattern, you can sanity-check your answers fast.
Flashcards work – test yourself on both the square and the root at once, not just one direction.
Picture it. A 5×5 grid for √25 makes the whole idea concrete instead of abstract, which helps a lot if you’re a visual thinker.

Square Roots vs. Cube Roots - Quick Clarification

Mixing up squaring and rooting. Squaring grows a number (for anything above 1); rooting shrinks it. It’s an easy slip, and it’s probably the single most common error students make with this topic.
Forgetting the negative root exists. Technically, 25 has two square roots: +5 and -5. Most everyday math just uses the positive one, but it’s worth knowing it’s there, especially once you hit algebra.
Rounding too soon. If a square root is just one step in a longer problem, hold off on rounding until the very end. Round early and those tiny errors add up.

Mistakes Worth Watching Out For

Since people mix these up constantly: a square root asks “what number times itself equals this?” A cube root asks the same question but three times over “what number times itself, times itself again, equals this?” So the cube root of 27 is 3 (since 3×3×3=27), while the square root of 27 is roughly 5.196. Different question, different answer – worth keeping straight, especially once you’re past basic algebra.

Conclusion

Square roots have a bit of a reputation for being confusing, but most of that comes down to not having a clear reference point. Once you’ve got the five perfect squares memorized and a rough sense of how to estimate the rest, this whole topic stops being intimidating pretty fast.

Keep this chart bookmarked, run through the estimation method a few times until it feels natural, and square roots will go from “that thing I always mess up” to just another tool you reach for without thinking twice.

Frequently Asked Questions

What's the full list of square roots from 1 to 25?

√1=1, √2≈1.414, √3≈1.732, √4=2, √5≈2.236, √6≈2.449, √7≈2.646, √8≈2.828, √9=3, √10≈3.162, √11≈3.317, √12≈3.464, √13≈3.606, √14≈3.742, √15≈3.873, √16=4, √17≈4.123, √18≈4.243, √19≈4.359, √20≈4.472, √21≈4.583, √22≈4.690, √23≈4.796, √24≈4.899, √25=5.

Which numbers between 1 and 25 are perfect squares?

Just five: 1, 4, 9, 16, and 25.

Why aren't all square roots whole numbers?

Because not every number is the result of squaring an integer. Numbers like 2,3, 5, and 7 aren’t perfect squares, so their roots come out as never-ending decimals — we just round them.

Is there a shortcut for finding these without a calculator?

Yes — prime factorization for perfect squares, estimation (using nearby perfect squares) for everything else. Between the two, you can handle almost anything in this range.

Do I really need to memorize the whole chart?

Not really. Learn the five perfect squares, get comfortable with the estimation trick, and you can figure out the rest on the fly without ever memorizing all 25 values.