III: Exponents, Square Roots, and Scientific Notation

1. What is the square root of 64?

8

32

14

The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, the square root of 64 is 8 because 8 multiplied by itself equals 64.

Explanation

The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, the square root of 64 is 8 because 8 multiplied by itself equals 64.

2. 6²

6

12

36

The given sequence follows a pattern where each number is obtained by multiplying the previous number by a certain factor. In this case, the factor is 6. Starting with 6, each subsequent number is obtained by multiplying the previous number by 6. Therefore, 6 * 6 = 36, which is the correct answer.

Explanation

The given sequence follows a pattern where each number is obtained by multiplying the previous number by a certain factor. In this case, the factor is 6. Starting with 6, each subsequent number is obtained by multiplying the previous number by 6. Therefore, 6 * 6 = 36, which is the correct answer.

3. (-8)²

-16

16

64

The given expression (-8)2 means -8 raised to the power of 2. When a negative number is raised to an even power, the result is always positive. Therefore, (-8)2 equals 64.

Explanation

The given expression (-8)2 means -8 raised to the power of 2. When a negative number is raised to an even power, the result is always positive. Therefore, (-8)2 equals 64.

4. 10³

100

1000

10000

The given sequence consists of powers of 10. Starting with 10^0 (which is 1), each subsequent term is obtained by multiplying the previous term by 10. Therefore, the next term in the sequence after 100 is 1000.

Explanation

The given sequence consists of powers of 10. Starting with 10^0 (which is 1), each subsequent term is obtained by multiplying the previous term by 10. Therefore, the next term in the sequence after 100 is 1000.

5. The preschool children needed a play-area with an area of 81 feet to accommodate the number of students enrolled in the class. If the room is in the shape of a square, what is the length of each wall?

40.5 ft

9 ft

3 ft

Since the room is in the shape of a square, all sides have the same length. To find the length of each wall, we need to find the square root of the total area. The square root of 81 is 9, so each wall of the play-area would be 9 feet long.

Explanation

Since the room is in the shape of a square, all sides have the same length. To find the length of each wall, we need to find the square root of the total area. The square root of 81 is 9, so each wall of the play-area would be 9 feet long.

III: Exponents, Square Roots, And Scientific Notation