Digits, Grade 8, Volume 1, Homework Helper
• 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 cm2. The area of the circular face of the round peg is 5 cm2. Will the round peg fit through the square hole? Use π = 3.14. Round to the nearest hundredth as needed.

End ofPage 39