1. If x = 36 and y = 25, is square root of x plus y end root rational or irrational? Simplify your answer.
2. After an accident, police can use the formula v equals 2 , square root of 5 l end root to estimate the speed, v, in miles per hour, that a car was traveling by measuring the length of the skid marks, L, in feet.
a. Estimate the speed of a car that left skid marks 65 ft long. Round to the nearest tenth as needed.
b. If the posted speed limit is 40 mi/h, was the car speeding?
3. Write 0.87 as a fraction in simplest form.
4. Write 0. , 72 bar as a fraction in simplest form.
5. Is square root of x squared , plus , y squared end root rational or irrational when x = 14 and y = 8? If you pick a whole number value for x, can you always find a whole number value for y to make the expression a rational number? Explain.
6. A couple wants to enclose a square garden with area 141 ft2. The wife says that they need about 47.6 ft of fence. The husband disagrees. He says they need about 11.9 ft of fence.
a. Who is correct?
b. What error did the person who found the incorrect length make?
A. The person divided the area of the garden by 4 to find the side length.
B. The person added 4 to the side length instead of multiplying by 4 to find the perimeter.
C. The person squared the area instead of finding the square root to find the side length.
D. The person found the side length of the garden, not the perimeter.
c. Explain how you found the correct length of fence that the couple needs.
7. Think About the Process The length of a rectangle is twice the width. The area of the rectangle is 90 square units. Notice that you can divide the rectangle into two squares with equal area.
a. How can you estimate the side length of each square?
A. Estimate square root of 90 over 4 end root , . .
B. Estimate square root of 90 . .
C. Estimate square root of 45 . .
D. Estimate square root of 45 over 4 end root , . .
b. Estimate the length and width of the rectangle.
8. Error Analysis Your teacher asks you to write 5.75 × 10−4 in standard form. Your classmate gives an incorrect answer of 0.0000575.
a. Write 5.75 × 10−4 in standard form.
b. What was your classmate's likely error?
A. Your classmate moved the decimal point 1 extra place to the left.
B. Your classmate moved the decimal point 2 extra places to the left.
C. Your classmate moved the decimal point 1 extra place to the right.
D. Your classmate moved the decimal point 2 extra places to the right.