What Does Square Root Calculator Do?

The calculator helps users to calculate the square root of a number with ease and accuracy. No matter how smaller or bigger the number you enter, the sqrt calculator will take instants to calculate its accurate second root, and shows step wise calculations for easy understanding.

Steps to Using Square Root Calculator

A couple of steps and you get the results on your screen.

1. Enter the number
2. Click ‘Calculate’
3. Get square root value with steps

It’s that simple!

↪ ️ Note: Please avoid calculating sqrt of a Negative Number, as it is not actually possible.

Why Use Our Square Roots Calculator?

• Instant, accurate results
• Supports decimals, fractions, variables
• Works as a simplifier and solver
• Easy to use and beginner-friendly
• Ideal for academic, learning, and professional use

What Is a Square Root?

A square root is a value that, when multiplied by itself, gives the original number. The square root symbol (√) and the function name sqrt are commonly used in mathematics:

Example:

√x = the number which, when squared, results in x.

How to Find Square Root of a Number?

Finding the square root means determining a number that, when multiplied by itself, equals the original value.

In math terms, it is the inverse operation of squaring and is represented by the radical symbol (√).

Common Methods

1. The Prime Factorization Method

This is the best method for perfect squares (like 144, 625, or 900). It involves breaking the number down into its smallest building blocks.

• Step 1: Divide the number into prime factors.
• Step 2: Group the same factors into pairs.
• Step 3: Take one number from each pair and multiply them together.

Example: Find \(\sqrt{144}\)

1. Factors of 144: 2x2x2x2x3x3
2. Group them: (2x2)x(2x2)x(3x3)
3. Pick one from each pair: 2x2x3 = 12

2. The Long Division Method

This is the most "exact" manual method for non-perfect squares or decimals (like $\sqrt{7}$ or $\sqrt{520}$). It works similarly to long division but uses different rules.

• Step 1: Pair digits from right to left (e.g., $5, 20$).
• Step 2: Find the largest number whose square is less than or equal to the first group.
• Step 3: Subtract, bring down the next pair, and double the divisor.

3. The Estimation Method (Newton-Raphson)

We use the formula:

\(x_{n+1}=\dfrac{1}{2}\left(x_{n}+\dfrac{S}{x_{n}}\right)\)

Where S=10, and \(x_[n}\) is our guess.

Iteration 01:

Choose the nearest perfect second root as your first guess:

\(x_{o}=3\) and \(3^{2}=9\)

\(x_{1}=\dfrac{1}{2}\left(3+\dfrac{1}{3}\right)\)

\(x_{1}=\dfrac{1}{2}\left(3+3.333\right)\)

\(x_{1}=3.166\)

Iteration 02:

Use 3.166 as a new guess to ensure higher accuracy.

\(x_{2}=\dfrac{1}{2}\left(3.166+\dfrac{10}{3.166}\right)\)

\(x_{2}=\dfrac{1}{2}\left(3.166+3.1579\right)\)

\(x_{2}=3.1622\)

Use Cases of Square Root Calculator

✔ School and College Students

• Solving algebra and geometry problems
• Understanding square roots for exams
• Checking manual calculations

✔ Teachers and Tutors

• Demonstrating calculations
• Creating teaching material
• Providing examples quickly

✔ Engineers and Professionals

• Working with square root formulas
• Applying values in structural design, physics, math, and science

✔ Researchers and Data Analysts

• Handling statistical formulas
• Square-root-based normalization, variance, and deviation calculations

✔ Everyday Users

• Quick evaluations
• Scientific curiosity
• Learning how square roots work

Faqs

Does the calculator support fractions and decimals?

Yes. You can calculate the square root of whole numbers, fractions, and decimals.

Is this calculator suitable for learning purposes?

Absolutely. It’s ideal for students learning how to do square root, simplifying expressions, or understanding manual and automated methods.

Does the tool show exact and simplified values?

Yes, where possible it shows:

• Exact decimal value
• Simplified radical form

Square Root Table

Important References

• Vedantu (n.d.) Square Root Calculator Online – Free with Formula & Steps. Available at: https://www.vedantu.com/calculator/square-root.

• Cuemath (n.d.) Formula, Examples | How to Find/Calculate Square Root? Available at: https://www.cuemath.com/algebra/squares-and-square-roots/ 

• Wikipedia (n.d.) Square root algorithms. Available at: https://en.wikipedia.org/wiki/Square_root_algorithms

• Khan Academy (n.d.) Square roots review (article). Available at: https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-roots/a/square-roots-review