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Square Root Calculator

Free online tool that helps you find the square root of a given number (x).

x
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How to calculate a square root?

One of the most common methods to calculate a square root is the long division method. Here are the steps to calculate a square root using the long division method:

  1. Write the number whose square root you want to find.
  2. Pair the digits of the number starting from the right. If there are an odd number of digits, then the leftmost digit will form a pair with a zero.
  3. Starting from the leftmost pair, find the largest number whose square is less than or equal to the pair. This will be the first digit of the square root.
  4. Subtract the product of the digit found in step 3 and itself from the pair, and bring down the next pair of digits (if any).
  5. Double the digit found in step 3, and write it as the divisor next to the remainder obtained in step 4.
  6. Divide the new dividend by the new divisor to obtain the next digit of the square root.
  7. Repeat steps 4 to 6 until you obtain the desired number of digits of the square root.

Here's an example to illustrate the process:

Let's calculate the square root of 784.

  1. Write the number: 784
  2. Pair the digits: 7|84
  3. Find the largest number whose square is less than or equal to 7. The largest number whose square is less than or equal to 7 is 2, so the first digit of the square root is 2.
  4. Subtract: 7 - 4 = 3. Bring down the next pair of digits: 38.
  5. Double: 2 x 2 = 4. Write it as the divisor next to the remainder: 3|38, 4.
  6. Divide: 34 ÷ 4 = 8. Write 8 as the next digit of the square root.
  7. Repeat:
    • New dividend: 38. Bring down the next pair of digits: 384.
    • Double: 2 x 2 = 4. Write it as the divisor next to the remainder: 38|4, 4.
    • Divide: 344 ÷ 44 = 7. Write 7 as the next digit of the square root.

Therefore, the square root of 784 is 28.

What is square root?

The square root of a number is a value that, when multiplied by itself, gives the original number. In other words, the square root of a non-negative number x is a non-negative number y such that y times y equals x.

For example, the square root of 25 is 5 because 5 times 5 equals 25. Similarly, the square root of 4 is 2 because 2 times 2 equals 4.

The symbol used to represent the square root operation is √, and the number inside the symbol is called the radicand. For example, √25 means the square root of 25.

Square root of 1-20

√11
√21.414214
√31.732051
√42
√52.236068
√62.44949
√72.645751
√82.828427
√93
√103.162278
√113.316625
√123.464102
√133.605551
√143.741657
√153.872983
√164
√174.123106
√184.242641
√194.358899
√204.472136