Find the square root by the division method.

646416

Square root of 646416 = 804

∴ square root of 646416 = 804

Step 1: Place a bar over every pair of digits starting from the one’s digit

Step 2: Find the largest number whose square is ≤ the number under the extreme left bar (8² < 64 < 9²). Take this number as the divisor and the quotient with number under extreme left bar as the dividend. Divide and get the remainder(0 in this case).

Step 3. Bring down the number under the next bar(i.e.,64 in this case) to the right of the remainder. So the new dividend is 064.

Step 4. Double the divisor and place this digit at ten’s place of new divisor (8+8 in this case)

Step 5. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 160 × 0 = 0. Get the remainder.

Step 6. Double the divisor once again and place this digit at ten’s place of new divisor (160+0in this case)

Step 7. Guess the largest possible digit to fill the unit’s digit of new divisor which also become the new digit in the quotient, such that new divisor is multiplied to the new quotient the product is ≤ the dividend.

In this case 1604 × 4 = 6416. Get the remainder

Step 8. Since the remainder is 0 and no digits are left in the given number.

∴ = 804