Question

How does one convert the square root of the number $32$ into a decimal number without using a calculator ?

Answer 1

Hint: When we have to convert the square root of the given number into a decimal number then we have a method known as long division method , this method provides a way to represent the square root of the number into decimal forms. This method is quite confusing but accurate.

Complete step by step solution:
We have to convert the square root of the given number that is $32$ into decimal number without using calculator ,
Let us do this with long division method ,
Now take the number $32$ . Now place a bar over the pair of numbers as $\overline{32}$ ,
Now take the largest number whose square is less than or equal to the number. Now divide the number with the largest number whose square is less or equal to zero,

Now, we further divide the remainder with the updated divisor that is by adding the unit place the pervious divisor itself and if the remainder is less than the updated divisor then put double zero and decimal to the quotient ,

Now, we have to find the largest number for divisor which we can put at the unit place of the divisor such that the largest number when multiplied by the divisor gives the result equal or less than the dividend .

Again, we further divide the remainder with the updated divisor that is by adding the unit place the pervious divisor itself and if the remainder is less than the updated divisor then put double zero and decimal to the quotient if no decimal is there ,

Now, we have to find the largest number for divisor which we can put at the unit place of the divisor such that the largest number when multiplied by the divisor gives the result equal or less than the dividend .

We get the solution that is the quotient of the above long division.

Therefore, we can say that the square root of the given number $32$ is $5.65$

Note: If any given number can be represented as a product of prime numbers. This method of expressing a given number in terms of the product of prime numbers is termed as the prime factorization method. We also have another long division method which is a bit confusing .