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Square Root Calculator

Use our free Square Root Calculator to quickly calculate square roots, squares, and simplified roots with step-by-step results.

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Finding the square root of a number sounds hard. But it doesn’t have to be. Our Square Root Calculator makes it simple. Enter a number, hit calculate, and you’ll get the answer in seconds. Whether you want to check the square root of 200,000 or just √3, this tool gives you quick and accurate results.

What is a Square Root?

A square root is the opposite of squaring a number. If 5 × 5 = 25, then √25 = 5. In other words, the square root finds the number that, when multiplied by itself, gives the original value.

Formula for Square Root:

√n = n^(1/2)

Example:

√16 = 4 because 4 × 4 = 16

How to Calculate Square Roots Manually

There are different methods, but the most common is Newton’s Method.

Formula:

x₁ = ½(x₀ + n / x₀)

Here, x₀ is the guess and x₁ is the improved value. Repeating the process gives a closer answer each time.

Example for √10:

Start with guess x₀ = 3.

x₁ = ½(3 + 10/3) = 3.1666

Next round brings us closer: 3.1622

So √10 ≈ 3.1622

How to Use Our Square Root Calculator

  1. Enter any number in the box.
  2. Choose precision (number of decimal places).
  3. Click calculate.
  4. Get instant results with steps.

If you enter a negative number, the calculator will show complex values using “i”. If the number is a perfect square like 49, the result will be exact.

Examples with the Calculator

  • √3 ≈ 1.732
  • √200000 ≈ 447.214
  • √81 = 9 (exact)
  • (15)² = 225

The calculator also simplifies square roots. For example:

√72 = 6√2

Why Use This Calculator?

You’ll save time. No need to guess or use long division. It’s fast, accurate, and works with both small and very large numbers. Students, teachers, or anyone working with math will find it handy.

Final Verdict

The Square Root Calculator is more than a tool. It’s like a math buddy that gives you quick answers, exact squares, and even shows steps. Try it now and see how easy math can be.

FAQs

How do you calculate square root?

You can use Newton’s Method or a calculator. Our tool does it for you.

How to calculate √ in a calculator?

Most calculators have a √ button. Type the number, press √, and get the result.

What is the square root of 200000?

The square root of 200000 is about 447.214.

How to calculate √3?

√3 ≈ 1.732, and our calculator shows it instantly.