Question

Determine the square root of each number. a. 64 b. 81 c. 121 d. 169 e. 22.5 f. 400

Short answer

Question: Find the square root for each given number: a. 64, b. 81, c. 121, d. 169, e. 22.5, f. 400. Answer: a. √64 = 8, b. √81 = 9, c. √121 = 11, d. √169 = 13, e. √22.5 ≈ 4.74, f. √400 = 20.

Step-by-step solution

Understand the square root concept

The square root of a given number x is a number y such that if you multiply y by itself (y * y), you get the original number x. In other words, the square root of x undoes the squaring operation. We use the symbol √ to represent the square root.

Identify the perfect squares

Recognize the given numbers that are perfect squares. These are numbers that have an integer value as their square root. For a, b, c, and d, they are all perfect squares: a. 64 b. 81 c. 121 d. 169

Find the square root for perfect squares

For each perfect square, find the integer value that, when multiplied by itself, equals that number: a. √64 = 8 because 8*8 = 64 b. √81 = 9 because 9*9 = 81 c. √121 = 11 because 11*11 = 121 d. √169 = 13 because 13*13 = 169

Calculate the square root for a non-integer

For 22.5, we cannot find an integer square root. However, we can use a calculator or other technique (e.g. Newton's method) to find an approximate value for its square root: e. √22.5 ≈ 4.74

Find the square root for the last perfect square

Finally, find the integer square root for the number 'f': f. √400 = 20 because 20*20 = 400 Now the student has found the square roots for all given numbers.