💡 How to Use This Lesson
Click any card above or use the tabs to navigate. The Explorer tab lets you tap any perfect square to see it visually. After the lessons, take the Quiz to test your GED readiness!
The square root of a number is the value that, when multiplied by itself, gives you that number.
If n × n = x, then √x = n
3² = 3 × 3 = 9 ↔ √9 = 3
Just like multiplication and division undo each other, squaring and square roots undo each other.
√9 is read as "the square root of 9." The number under the √ symbol is called the radicand.
If you can make a perfect square with 9 tiles arranged 3 × 3, then √9 = 3. The side length of the square IS the square root!
What number times itself equals 16? That number is √16.
A perfect square is a number that has a whole-number square root. 9, 25, 49, 64, 100, and 144 are all perfect squares.
What is √121? (Think: what number × itself = 121?)
As the number gets bigger, the grid gets bigger. The side length of the square = the square root. This is why they're called "square" roots!
√(a/b) = √a ÷ √b — find the square root of the numerator, then find the square root of the denominator.
√16 = 4 (because 4 × 4 = 16)
√25 = 5 (because 5 × 5 = 25)
√1 = 1 (because 1 × 1 = 1)
√4 = 2 (because 2 × 2 = 4)
What is √(9/25)? (√9 = ?, √25 = ?)
| Number (n) | Squared (n²) | Square Root (√n²) |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 4 | 2 |
| 3 | 9 | 3 |
| 4 | 16 | 4 |
| 5 | 25 | 5 |
| 6 | 36 | 6 |
| 7 | 49 | 7 |
| 8 | 64 | 8 |
| 9 | 81 | 9 |
| 10 | 100 | 10 |
| 11 | 121 | 11 |
| 12 | 144 | 12 |
| 13 | 169 | 13 |
| 14 | 196 | 14 |
| 15 | 225 | 15 |
🔑 Tip: Work Backwards!
On the GED, if you see √49, ask yourself: "What number squared equals 49?" Run through your list: 6²=36, 7²=49 ✅ — the answer is 7!
√1=1, √4=2, √9=3, √16=4, √25=5, √36=6, √49=7, √64=8, √81=9, √100=10, √121=11, √144=12. These show up most often!
√(x²) = x. If you see √(5²), the answer is simply 5. The square root undoes the square!
√50 is not a whole number, but you know √49=7 and √64=8, so √50 is between 7 and 8 — closer to 7. On the GED, look for the two perfect squares it falls between.
√(a/b) = √a / √b. Only works when both top and bottom are perfect squares!
The GED only asks for the principal (positive) square root. √9 = 3, never −3, on GED questions.