Square Root Calculator
Find the square root or any root of a number, with the simplified radical form such as 6√2.
Root
8.485281374
- Exact form
- 6√2 in simplest radical form
- The number squared
- 5,184
The 2-th root of 72 is shown above.
Calculation breakdown
| Step | Formula | Result |
|---|---|---|
| Root | 72 ^ (1 ÷ 2) | 8.48528137 |
How it works
Enter a number. The root is 2 for a square root, or choose 3, 4 or higher.
Worked example
The square root of 72:
- Decimal: 8.485281374
- The largest perfect square that divides 72 is 36 (72 = 36 × 2)
- Simplified form: √72 = 6√2
Sources
Frequently asked questions
What is a square root?
The square root of a number is the value that multiplied by itself gives that number. The square root of 144 is 12 because 12 × 12 = 144. Every positive number has a positive and a negative square root, and the calculator shows the positive one.
How do you simplify a square root?
Find the largest perfect square that divides the number and take its root outside the radical. 72 = 36 × 2, so √72 = √36 × √2 = 6√2.
Can I take other roots?
Yes. Change the root to 3 for a cube root, 4 for a fourth root and so on, up to 20. The cube root of 54 simplifies to 3∛2.
What is the square root of a negative number?
There is no real answer, because no real number squared is negative. The result is an imaginary number, so √−4 = 2i. Odd roots of negative numbers are real, so the cube root of −27 is −3.
How can I tell if a number is a perfect square?
If its square root is a whole number, it is a perfect square. The calculator marks perfect squares, such as 144 and 169.