Find the square root of 79.21 using the long division method.

To find the square root of 79.21 using the long division method, follow these steps:

Step 1: Set Up the Problem

Write 79.21 as 7921.00, adding two decimal places for accuracy. Pair the digits from right to left: (79)(21)(00).

Step 2: Find the Largest Square

Determine the largest square less than or equal to 79. The largest is 8, since 8 x 8 = 64.

• Write 8 above the first pair (79).
• Subtract 64 from 79, leaving 15.

Step 3: Bring Down the Next Pair

Bring down the next pair (21) next to 15, making it 1521.

Step 4: Double the Quotient

Double the current quotient (8) to get 16. Now, find a digit (x) such that (160 + x) x x is less than or equal to 1521.

• Testing x = 9: (169) x 9 = 1521, which works perfectly.

Step 5: Complete the Calculation

Write 9 next to 8 in the quotient, making it 8.9. Subtract 1521 from 1521, resulting in 0.

Final Result

The square root of 79.21 is 8.9.