Unit 2 the number system rational and irrational numbers practice
1. Determine whether each of the following numbers is rational or irrational.
a) √9
b) -4
c) 0
d) π
2. For each rational number below, write it as a fraction in simplest form.
a) 0.75
b) -1.2
c) 2.5%
d) -0.625
3. Express each irrational number below as a decimal to the nearest hundredth.
a) √2
b) 3√5
c) √7
d) π
4. Determine whether each of the following numbers is a terminating or repeating decimal.
a) 0.25
b) 0.333...
c) 0.987654321
d) 0.142857142857...
5. Compare the following pairs of numbers and determine which is greater.
a) √10 or π
b) 2.8 or -3.2
c) 0.5 or 0.75
d) -√5 or -2
6. Simplify each expression below.
a) √25 (4 + √9)
b) √64 / √4
c) √(36 - 16)
d) √(3^2 + 4^2)
7. Determine whether each of the following statements is true or false.
a) The sum of a rational number and an irrational number is always irrational.
b) All integers are rational numbers.
c) The product of two irrational numbers is always irrational.
d) The square root of a negative number is always an imaginary number.
8. Solve the following equations for x.
a) √(x + 5) = 3
b) 2x - √(3x + 4) = 0
c) 2√x + 5 = 9
d) 4(3 - 2x) = √(x + 7)
9. A rectangular field measures 8 meters by 12 meters. Find the length of the diagonal of the field.
10. A square has an area of 36 square meters. Find the length of each side of the square.
Sure! I can help you with practicing the concepts related to rational and irrational numbers in the number system. Here are some step-by-step practice questions for you:
1. Identify the following numbers as rational or irrational:
a) √16
b) 2.5
c) 3/4
d) π
2. Simplify the following expressions:
a) 3 + √9
b) √25 - 4
c) 2/3 + √16
d) √49 - √9
3. Determine whether the following statements are true or false:
a) The sum of two irrational numbers is always irrational.
b) The product of two irrational numbers is always irrational.
c) The difference of two rational numbers is always rational.
d) The quotient of two irrational numbers is always irrational.
4. Order the following numbers from least to greatest:
a) π, 0.7, √2, 1/2, √5
5. Evaluate the following expressions:
a) (2/3)^2
b) (√9)^3
c) √(16/4)
d) 3(√5 + 1)
I hope these practice questions help you strengthen your understanding of rational and irrational numbers in the number system. Let me know if you need help with any specific question!