Mike is building a frame for a painting that he has bought. The painting is in the shape of a square with an area of 75 square inches. How long should each side of the frame be if he wants to build the smallest frame he can to fit the painting?

A. Between 6 and 7 inches
Incorrect. The square root of 75 is greater than 7. The frame would be too small for the painting.

B. Between 7 and 8 inches
Incorrect. The square root of 75 is greater than 8. The frame would be too small for the painting.

C. Between 8 and 9 inches
Correct! The square root of 75 is between 8 and 9. This would build the smallest frame that would still fit the painting.

D. Between 9 and 10 inches
Incorrect. The square root of 75 is less than 9. This frame would fit the painting, but it is not the smallest frame that would fit.

A. 6 units
Incorrect. This is how much the x-coordinate changed.

B. 9 units
Incorrect. This is how much the y-coordinate changed.

C. 11 units
Correct! The square root of 117 is closest to 11.

D. 15 units
Incorrect. This adds together the x and y change.

Four students are playing a game in their math class. Each student has four cards with irrational numbers on them. The teacher picks a whole number, and the students play the card in their hand that is closest in value to the whole number without going over.

Tom has the following four cards —

If the teacher picks the number 4, which card should Tom play?

A
Correct! This irrational number is the closest to 4 without going over.

B
Incorrect. This irrational number is the closest to 4, but it is greater than 4.

C
Incorrect. The number under the square root is 4 + 4; it would have to be 4 x 4.

D
Incorrect. The number under the square root is the square root of 4; it would have to be four squared.

What is the value of the circumference of the circle with a diameter of d = 2 inches?

A. Between 3 and 4
Incorrect. Remember, the value of π is a little bit more than 3.

B. Between 4 and 5
Incorrect. Remember, the value of π is a little bit more than 3.

C. Between 5 and 6
Incorrect. Remember, the value of π is a little bit more than 3.

D. Between 6 and 7
Correct! The value of π is a little bit more than 3.

The following picture shows a square with a total area of 56 square meters.

Which is closest to the approximate value of the side s?

A. 7 meters
Incorrect. The square root of 56 is greater than 7.

B. 7.5 meters
Correct! The square root of 56 is approximately between 7 and 8.

C. 8 meters
Incorrect. The square root of 56 is less than 8.

D. 8.5 meters
Incorrect. The square root of 56 is less than 8.5.