Squaring a Number

1. True or false: To square a number, multiply it by itself. For example, if you have the number 4, squaring it means 4 multiplied by 4, which equals 16.
   

• True

• False

Answer explanation

When you square a number, you multiply it by itself. For example, if you have the number 4, squaring it means 4 multiplied by 4, which equals 16. So, 4² = 4 × 4 = 16.

1. True or false: When you square a negative number, you get a negative result because a negative times a negative gives a negative. For example, if you square -3, you get -3 × -3 = -9.

• True

• False

Answer explanation

When you square a negative number, you get a positive result because a negative times a negative gives a positive. For example, if you square -3, you get -3 × -3 = 9, which is positive. So, (-3)² = -3 × -3 = 9.

1. True or false: A perfect square is a number that you get when you multiply a whole number by itself. For instance, 25 is a perfect square because it can be obtained by multiplying 5 (a whole number) by itself: 5 × 5 = 25.
   

• True

• False

Answer explanation

A perfect square is a number that you get when you multiply a whole number by itself. For instance, 25 is a perfect square because it can be obtained by multiplying 5 (a whole number) by itself: 5 × 5 = 25.

1. The area of a square can be found by squaring the side length. A square has a side length of 8 ft. What equation represents the area of the square?

• 1. A = 8² = 16

• 1. A = 8 × 4 = 32

• 1. A = 8² = 64

• 1. A = 8 × 2 = 16

Answer explanation

The formula for finding the area of a square is given by A = side² = side length × side length. In this case, the side length is 8 ft. So, the correct equation is A = 8² = 8 × 8 = 64.

1. Evaluate 7².

• 14

• 49

• 21

• 56

Answer explanation

To find 7², you need to multiply 7 by itself: 7 × 7 = 49. So, 7² = 49.

1. Evaluate (-11)².

• -22

• 112

• 33

• 121

Answer explanation

To find (-11)², you need to multiply -11 by itself: -11 × -11 = 121. So, (-11)² = 121.

1. Evaluate -12².
   

• -144

• 144

• -24

• 24

Answer explanation

To solve -12², you first square 12 (12 × 12), which equals 144. Then, you add the negative sign, resulting in -144.

1. Evaluate (5/9)².

• 25/18

• 1/25

• 25/81

• 81/25

Answer explanation

To find (5/9)², you square both the numerator and the denominator separately: (5²)/(9²) = 25/81. So, (5/9)² = 25/81.

1. Evaluate (-0.4)².

• -0.08

• 0.16

• 0.08

• -0.16

Answer explanation

To solve (-0.4)², you square the decimal value: -0.4 × -0.4 = 0.16. So, (-0.4)² = 0.16.

1. Evaluate -(11/12)².

• -121/144

• 121/144

• -121/132

• 121/132

Answer explanation

To calculate -(11/12)², first square the fraction. You square both the numerator and the denominator separately: (11²)/(12²) = 121/144.Then, add the negative sign, resulting in -(121/144). So, -(11/12)² = -121/144.