Objectives: To approximate square roots by (1) using a square root table (2) by the divide-and-average method (3) after simplifying radicals

The value of the square root of a whole number can either be found by using a square root table or by using a calculator. The divide and average method can also help find square roots.

When possible, simplify a radical before using the square root table or a calculator.

Examples:
a.) Approximate to the nearest tenth. Use the divide and average method:
1. Locate 32 between two perfect squares: 5 < < 6.
2. Divide 32 by any number between 5 and 6: 32 / 5.5 = 5.81...
3. Average 5.5 and 5.81 to find a new divisor: (5.5 + 5.81)/2 = 5.65
4. Divide 32 by 5.65. The divisor and the quotien agree to the nearest tenth, which is close enough.
Thus, is approximately 5.7

b.) The area of a square field is 53 sq. meters. Find the length of a side of the field correct to the nearest tenth of a meter.

 A = s²
53 = s²
 s =
 s = 7.280...
Thus, the length of a side of the field is about 7.3m.