Square Root Calculator
Square Root Calculator
Calculate the principal square root of any zero or positive number. Enter a value to find the non-negative number that produces it when multiplied by itself.
Enter your values
Enter a zero or positive number and select Calculate.
Square Root Calculator – Calculate the Square Root of a Number
Use this free Square Root Calculator to find the principal square root of a number quickly. The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 64 is 8 because 8 × 8 = 64. This tool accepts zero and positive numbers and calculates the non-negative real square root.
How to Use the Square Root Calculator
- Enter the number whose square root you want to calculate.
- Make sure the number is zero or positive for a real-number result.
- Select the Calculate button to display the square root.
- Use Clear to remove the previous input and calculate another value.
Square Root Formula
Formula: \(r = \sqrt{x}\), where \(r \geq 0\) and \(r^2 = x\).
Here, \(x\) is the number (radicand), and \(r\) is its principal square root. The principal square root is always non-negative.
Worked Examples
Example 1: Square root of 25
\(\sqrt{25} = 5\), because \(5 \times 5 = 25\).
Example 2: Square root of 2.25
\(\sqrt{2.25} = 1.5\), because \(1.5 \times 1.5 = 2.25\).
Example 3: Square root of 0
\(\sqrt{0} = 0\), because \(0 \times 0 = 0\).
Perfect Squares and Non-Perfect Squares
A perfect square is a number that can be written as an integer multiplied by itself, such as 1, 4, 9, 16, 25 and 36. Their square roots are whole numbers. Numbers such as 2, 3 and 10 are not perfect squares, so their square roots are non-terminating decimal values. A calculator provides a useful decimal approximation for these values.
Where Are Square Roots Used?
Square roots are used in mathematics, geometry, engineering, statistics and everyday calculations. For example, the side length of a square can be found by taking the square root of its area. The Pythagorean theorem also uses square roots to calculate the length of a side in a right-angled triangle.
Important Note About Negative Numbers
This calculator is designed for real-number results. A negative number does not have a real square root because the square of any real number is zero or positive. Complex-number calculations use imaginary numbers and are outside the scope of this calculator.
Frequently Asked Questions
1. What is a square root?
A square root of a number is a value that, when multiplied by itself, equals that number. The principal square root is the non-negative value.
2. How do I calculate a square root?
Enter a zero or positive number in the calculator and select Calculate. The result is the principal square root.
3. What is the square root of 64?
The square root of 64 is 8 because 8 multiplied by 8 equals 64.
4. What is the square root of zero?
The square root of zero is zero, since 0 × 0 = 0.
5. Can I calculate the square root of a negative number?
Not as a real number. The square of every real number is non-negative. Negative inputs require complex-number mathematics.
6. What is a perfect square?
A perfect square is an integer that is the product of another integer multiplied by itself, such as 9, 16 or 25.
7. Is the square root of every positive number a whole number?
No. Only perfect squares have integer square roots. For example, √2 is approximately 1.4142.
8. What is the difference between a square and a square root?
Squaring a number means multiplying it by itself. Taking a square root reverses that operation for a non-negative number.
9. What is the square root symbol?
The square root symbol is √. In √25, the number 25 is called the radicand.
10. Can this calculator handle decimal numbers?
Yes. Enter a positive decimal number, such as 2.25, to calculate its square root.
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