Square Root Calculator
Enter any number to find its square root instantly. This tool returns the principal root and explains whether the number is a perfect square.
What is a square root?
A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 49 is 7, because 7 × 7 = 49.
Most calculators show the principal square root, which is the non-negative result. So even though both +7 and -7 satisfy x² = 49, the square root symbol √49 returns 7.
How to find square root with this calculator
Step-by-step
- Type a number in the input box (whole number or decimal).
- Set your preferred decimal precision.
- Click Calculate Square Root.
- Read the result and check the verification line.
This is the fastest way to answer questions like “what is the square root of 81?”, “how to find square root of decimals,” or “is this number a perfect square?”
How to find square root without a calculator
1) Use memorized perfect squares
If your number is a perfect square, the answer is exact and immediate.
- 1² = 1
- 2² = 4
- 3² = 9
- 4² = 16
- 5² = 25
- 6² = 36
- 7² = 49
- 8² = 64
- 9² = 81
- 10² = 100
2) Prime factorization method (great for integers)
Break the number into prime factors, then pair matching factors:
- Example: 144 = 2 × 2 × 2 × 2 × 3 × 3
- Pair them: (2×2), (2×2), (3×3)
- Take one from each pair: 2 × 2 × 3 = 12
- So, √144 = 12
3) Estimation method (for non-perfect squares)
Find the two nearest perfect squares around the number.
- For √50, nearby squares are 49 and 64.
- Since √49 = 7 and √64 = 8, then √50 is between 7 and 8.
- Because 50 is close to 49, the value is close to 7 (about 7.071).
Worked examples
Example 1: √64
64 is a perfect square. 8 × 8 = 64, so √64 = 8.
Example 2: √72
72 is not a perfect square. You can simplify it:
- 72 = 36 × 2
- √72 = √36 × √2 = 6√2
- Decimal form is approximately 8.485281
Example 3: √0.36
0.36 = 36/100, so:
- √0.36 = √36 / √100 = 6/10 = 0.6
Common mistakes to avoid
- Confusing square root with divide-by-2: √100 is 10, not 50.
- Forgetting principal root convention: the symbol √x returns the non-negative value.
- Rounding too early: keep extra digits during intermediate steps.
- Ignoring domain in real numbers: negative numbers have no real square root.
Square root calculator FAQ
Can I find square roots of decimals?
Yes. The calculator accepts decimal values and returns a rounded result based on your selected precision.
What if the number is negative?
In real numbers, square roots of negative numbers do not exist. In complex numbers, √-a = i√a.
How do I verify the answer?
Multiply the calculated root by itself. If it matches the original value (or is extremely close after rounding), the result is correct.
Final takeaway
If you need speed and accuracy, use the square root calculator above. If you want stronger math skills, practice perfect squares, factorization, and estimation. Together, these methods make finding square roots simple in homework, exams, coding, finance, and everyday problem-solving.