# Find the square root of the following number by Division method: 529

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**Hint:**Here, use the division method by grouping 529 as 5 29 and do the process of division. At the last to check whether the result obtained is correct or not, multiply the result by itself to get 529.

**Complete step by step answer:**

Here, we have divided the solution into steps.

Step I: Write the given number 529 in two parts as 5 29 by grouping the numbers in pairs, always starting from the right end of the given number. (Here, start from the number 5 ).

Step II: Find the greatest positive number whose square is less than (or equal to) 5. Here it is 2, as ${2^2} < 5$.

Step III: Write 2 in place of the quotient (or on the top), and also write 2 as a divisor.

Step IV: Multiply 2 on the top with the divisor 2 and write the result i.e. 4 under 5 and subtract as we do in the division. The remainder obtained is 1.

Step V: Write down the pair 29 by the side of the remainder 1, we get 129.

Step VI: Double 2 and take the resulting number 4. Find that number y such that 4y × y is just less than or equal to 129.

Here, we have 42×2=84 and 43×3=129 and so y = 3.

Step VII: Now, we have 43 as the next divisor and put 3 on the top along with 2. Write the product 43 × 3=129 under 129 and subtract again as we do in division. Since the remainder is 0, the division is complete. Hence, $\sqrt {529} $ =23

See below:

Also, 23 × 23 = 529, hence our answer is correct.

**Note:**

The division method is useful for finding square roots of large numbers as the factorization method is lengthy for big numbers.