Exponents
How do you express 2 x 2 x 2 in exponent form?
2^3
What is the square root of 4?
2
Which of the following is a perfect square? Answer and explain. A. 11 B. 20 C. 4 D. 8
C. because 2 x 2 = 4.
The sides of a square are 4 inches. What is the area of the square?
The area is 16 inches.
How do you say 6^5?
"Six to the fifth power."
What is 4^5 in expanded form?
4 x 4 x 4 x 4 x 4
Solve. √49 =
7
What is the perfect square of 8? Explain.
64 because 8 x 8 = 64.
A square has an area of 81 centimeters. What is the length of its sides?
The sides are 9 centimeters.
What do you need to do to the area of a square to find the length of its sides?
Take the square root of the area.
Solve 2^4
16
What is the square root sign (√) called?
A radical
What are the two different ways you can say 5^2?
"Five to the second power" and "five squared"
What is the perimeter of a square with sides that are 5 inches?
The perimeter is 20 inches.
James makes 15^2 a week. How much does he make in 3 weeks?
James makes $675 in three weeks.
Solve 6^3
216
Solve. √9 x √121 =
33
Solve. (perfect square of 7) + (the perfect square of 3) =
49 + 9 = 58.
The length of a quadrilateral is 9 centimeters and the width is 8 centimeters. What is the area of the quadrilateral?
The area is 72 centimeters.
You would like to frame your artwork with fancy rope. The picture is 6 inches long and 7 inches wide. You want to buy 5 more inches than you need, just to be safe. How much rope do you need? Explain how you got your answer.
You will need 31 inches of rope. Since you are framing the picture, you need to find the perimeter. 6 + 6 + 7 + 7 = 26. You want to buy 5 extra inches to be safe. 26 + 5 = 31. That is why you will need to buy 31 inches of rope.
What is 4^3 plus 5^3
189
Marissa's mom offered her three different options for her weekly allowance. Her three options are: A. √36 x 2^2 dollars a week B. √9 x √121 dollars a week C. √169 x 2 dollars a week How much would she make with each option? Which option should she choose? Explain your work.
She should chose option B because she would earn $33 a week (√9 = 3, √121 = 11, and 3 x 11 = 33). If she chose option A, she would only make $24 dollars (√36 = 6, 2^2 = 4, and 6 x 4 = 24), and if she chose option C, she would only make $26 a week (√169 = 13, and 13 x 2 = 26).
Explain why we call it a "Perfect Square." Be specific!
When finding the area of a square, you multiply length times width. In a square, all four sides are equal. Therefore, when you find the area of a perfect square, you are multiplying the same number by itself.
You would like to tile the bathroom floor. The floor is 30 tiles long and 30 tiles wide. Is 95 tiles enough to tile the whole floor? Exactly how many tiles do you need?
95 tiles is not enough to tile the whole floor. You need exactly 900 tiles.
You just met Harry Potter and he gave you a magic coin! The coin doubles every day! On the second day, you have two coins and on the third day you have four coins. The equation for the third day is 2^2. Each coin is worth $10. How much money will you have on the 15th day? Explain how you got your answer.
You will have $163,840 on the 15th day. First, I found out how many coins you would have by solving 2^14 = 16,384. Next, I multiplied my answer by $10 by moving my decimal one place to the right, which gave me $163,840.