How to Find the Square Root of a Number: Calculator and Long Division Method Explained

Square Root

A value that, when multiplied by itself, gives the number under the radical sign.

The square root of a number is a value that when multiplied by itself, produces the original number. For example, the square root of 9 is 3 because 3 multiplied by itself equals 9.

The symbol used to represent the square root is √, and it is placed before the number we want to find the square root of.

To find the square root of a number, you can use a calculator or you can use the long division method. Here is an example of the long division method for finding the square root of 64:

1. Start with the number you want to find the square root of, which in this case is 64.
2. Divide the number into pairs, starting from the right-hand side. If there is an odd number of digits, add a 0 to the left-hand side to make it even. In this case, we have 6 and 4.
3. Find the largest perfect square that is less than or equal to the first pair. In this case, the largest perfect square less than or equal to 6 is 4.
4. Write the square root of the perfect square (in this case, 2) in the quotient above the first pair. Then write the remainder (2) to the right of the first pair.
5. Bring down the next pair of digits (in this case, just 4) to the right of the remainder to form a new number.
6. Double the root (in this case, 2) and write it next to itself. Then find the largest multiple of this doubled root that is less than or equal to the new number. In this case, the new number is 24 and the largest multiple of 4 that is less than or equal to 24 is 20. Write 4 and 5 (20 divided by 4) in the quotient and remainder positions respectively.
7. Repeat steps 5 and 6 until all digits have been used.

Therefore, the square root of 64 is 8.

It’s worth noting that some numbers have irrational square roots, which means they cannot be expressed as a finite decimal or a fraction. For example, the square root of 2 is an irrational number. The decimal representation of the square root of 2 goes on forever and never repeats.

More Answers: