Question

What is the step by step method of square root of 529 by pime factorization method?

Answer 1

1. 529
2. 23
3. 23
4. so here 23 is prime factor so by making pair 23 is in pair so it is square root of 529.
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Answer 2

solution

The use of the number of digits in square root of a number is useful in the following method

consider the following steps to find the square root of 529

Step 1

Place a bar over every pair of digits starting from the digit at ones place if the number of digits in its ok then the leftmost single- digit toowill be there about that we have 529

Step 2

Find the largest number whose square is less than or equal to the number under the extreme left bar (2²<5<3²).Take this number as the divisor and quotient with the number under the extreme left bar as the division (here 5).Divide and get the reminder (1 in this case)

Step 3

Bring the number under the next bar example 29 this case to the right of the reminder ,so the new divisor is 129

Step 4

Double the quotient and enter it with the blank on its right

Step 5

Guess a largest possible digit to fill in the blank which will also become the new digit in the quotient such that when the new divisor is multiplied to the new question the product is less than or equal to the dividend ,In this case 42×2=84

As 43×3=129,so we choose the new digits as 3.we get the reminder.

Step 6

Since, the reminder is 0 and no digits are left in the given number therefore

$\sqrt{529 = 23}$