9.
a. Is square root of y plus x plus z end root rational or irrational for x = 15, y = 22, and z = 14? Simplify your answer.
b. Is square root of y plus x plus z end root rational or irrational for x = 14, y = 25, and z = 10? Simplify your answer.
c. Find three different values that make the expression rational.
d. Find three different values that make the expression irrational.
e. Describe how you found these sets of numbers.
10. Write 1. , 48 bar as a mixed number in simplest form.
11. If x = 4 and y = 5, is square root of x squared , plus , y squared , plus 57 end root rational or irrational? Simplify your answer.
12. Think About the Process
a. Evaluate the expression square root of x cubed , plus , y squared , plus 5 end root for x = 3 and y = 2. Leave your answer in square root form.
b. How can you decide if the result is rational or irrational?
A. See if the value under the square root symbol is a perfect square or not.
B. See if the value under the square root symbol is positive or negative.
C. See if the value under the square root symbol is a whole number.
D. See if the value under the square root symbol is a rational or an irrational number.
c. Is the result rational or irrational?
13.
a. Challenge If x = 5, y = 6, and z = 2, is square root of x squared , plus , y squared , plus , z squared , plus 56 end root rational or irrational? Simplify your answer.
b. If the result is an irrational number, find values for x, y, and z that give a rational number.
c. Once you've found three values that give a rational number, find three other values for x, y, and z that give a rational number.
14. Challenge A toy has various shaped objects that a child is supposed to push through matching holes. The area of the square hole is 5 cm^{2}. The area of the circular face of the round peg is 5 cm^{2}. Will the round peg fit through the square hole? Use π = 3.14. Round to the nearest hundredth as needed.