Square Root Calculator

Square Root Calculator is a free online tool to find the square root, cube root, and nth root or radical of any given number.

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Stuck in finding the square roots for your mathematics homework? Get accurate and fast results with our square root calculator for free. Find square root, cube root, and nth root or radical of any given number. Also, you can add, subtract, multiply, and divide any two square root values.

Just enter the number for which you need to find the square root of and then simply press the "Calculate" button. The answer will be on your screen within seconds. It eliminates the difficulties you can face while solving on pen and paper. Make your calculations easier and faster using our tool.

Our tool also has two more functions. You can use it as a cube root calculator and nth root or radical calculator. Our tool has dedicated tabs for square, cube, and nth root calculation. So, it becomes a one-stop destination for all types of root calculations. In this article, we will know more about the features, use cases, and the algorithm used behind it. We also have elaborated on how you can use the calculator. This article will teach you everything and you will be able to use it easily every time.

What is Square Root?

A square root of a number can be defined as a number which when multiplied with itself gives that number. For example, if a number is 9 then its square root is 3. As when 3 is multiplied by 3, it gives 9.

The radical symbol (√) is used for denoting square root. It's also known as the "Root symbol" or "Surds".

Difference between Perfect and Non-perfect Square Numbers

• If a number is a perfect square it becomes very easy to find the square root of that number. Every perfect square ends with 0, 1, 4, 5, 6, or 9.
• Finding the square roots of non-perfect square numbers are difficult and we need to go for the long division method to find the square root of that number.

Our square root calculator works for both perfect and non-perfect squares.

How to Calculate Square Root?

If you ask for the simplest way to find the square root of a number then just use our free online square root calculator.

Along with that let's also learn about the standard mathematical approach to calculate the square root.

We have four methods to find the square root and they are as follows:

1. Long division method
2. Prime factorization method
3. Repeated subtraction method
4. Estimation method

Only the long division method is useful for calculating the square root of a non-perfect square. All three other methods can only be applied to perfect square numbers. If you are unsure whether a number is a perfect square or not you must go with the long division method. It can find the square root of perfect as well as non-perfect squares. However, the process is a bit complex than others.

Let's look at each method one by one.

1. Long Division Method

Long Division Method can give you the exact square root of any number. The process involves breaking down a large number into steps or parts.

1. Mark the pairs from the unit's end.
2. Look for a perfect square that is equal to or lower than the first pair. Remember that if we are selecting a lower perfect square, it should be the closest one to the first pair. Write the square root for it on the left side (Divisor).
3. Multiply above and add below with the same number (written on the left side). Leave some empty space after the digits are obtained.
4. Now, we just subtract the product from the number above it.
5. Get the next pair down and repeat the operations from step 3.
6. The moment we get 0 at the remainder and there are no more pairs left we will stop the process. The number on the top (Quotient) is the square root.

2. Prime Factorization Method

In this method, we break down the number into its prime factors. The most important thing to keep in mind while using prime factorization is that the number should be a perfect square.

1. Write down the prime factors of the number.
2. Take one factor from each pair of similar factors.
3. Multiply all the common factors (one from each pair).
4. The result so obtained is known as the square root.

Let's make it clearer through an example. Let's calculate the square root of 16. As 16 is a perfect square and we can use the prime factorization method.

The prime number representation will be as follows:

2 x 2 x 2 x 2 = 16

We can pair the first and second 2's together and remain as another pair. Out of both pairs we take 2 from each as a common factor and find the product to get 4. The square root of 16 is 4.

2 x 2 = 4 = √16

3. Repeated Subtraction Method

The process of the repeated subtraction method is quite easy. Just keep on subtracting consecutive odd numbers till you get zero. The odd number should be in order. Don't take a high jump to reach zero easily. There will be a time when you will reach zero and the number of steps to reach zero is the square root of the number. Remember, this method is only applicable for perfect square numbers.

Let's calculate the square root of 25 using the repeated subtraction method. In this method, we will subtract the values with odd numbers till we get zero.

First step: 25 – 1 = 24
Second step: 24 – 3 = 21
Third step: 21 – 5 = 16
Fourth step: 16 – 7 = 9
Fifth step: 9 – 9 = 0

So, the total number of steps = 5.

Hence, the square root of 25 is 5.

4. Estimation Method

There is no actual mathematical calculation involved in the Estimation Method. In this, you need to guess the value. However, this method is not recommended if you want accurate results. For approximation, you can surely go for it. Also, it's time-consuming as well as prone to errors.

Above all methods are just for your knowledge gain. You don't need to calculate the square root manually. Just keep our square root calculator handy. It will make your work easy, fast, and more accurate. Also, it will save you time and effort.

Features of Square Root Calculator

• Easy to use: Simple user interface and fewer buttons make the job easy. Just enter your number and tap Calculate. Answer within seconds!
• One-stop destination: No need to use different tools for different calculations. You can calculate the square root, cube root, and nth root at one place.
• Fast and accurate: Get 100% correct results within seconds.
• Absolutely free: Our tool is free forever. No hidden charges.
• No signup or installation required: Just visit the website and use it. Nothing to worry about.
• Additional arithmetic operations: You can also perform addition, subtraction, multiplication, and division. This feature is not for nth root and cube root calculator.

How to use Square Root Calculator?

This section explains how you can use the calculator to find the roots. As mentioned above, this tool is very easy to use. So, you will never find any difficulty while using it.

1. First of all, decide what you want to do and select the specific tab. For example, if you want to calculate the cube root then choose the "Cube Root" tab to open it. The tab which has been selected or active will turn orange and show the appropriate calculator below. Similarly, you can choose square root or nth root tabs if you want.
2. Enter the number to find the root in the input box. If you select the nth root tab then you will get two input areas. The first is for the value of "n". The second is for the number to find the root of.
3. Press the "Calculate" button to get the final results.
4. The root of the number will be displayed in the grey output box. Also, you can copy the final results using the "Copy" button.
5. The "Reset" button will clear the input and output and you can start the new calculation.

To perform arithmetic operations, press the "Expand" button. It will show drop-down options to select the operation. In addition, it will show another input box for entering the second operand. Now fill in all the values and press the "Calculate" button to get the final output. That's it.