Rational and irrational numbers practice
Sure! I can give you some practice problems to work on.
1) Classify the following numbers as rational or irrational:
a) 3.5
b) -2
c) √16
d) π
e) 0.123123123...
2) Simplify the following irrational expressions:
a) √25
b) √72
c) √27
d) ∛64
e) ∛125
3) Determine whether the following statements are true or false:
a) Irrational numbers can be expressed as fractions.
b) All rational numbers can be expressed as decimals.
c) The sum of a rational number and an irrational number is always irrational.
d) Squaring an irrational number always results in another irrational number.
e) The number 0.333... is irrational.
Take your time to solve these problems and let me know if you need any further assistance!
Sure! Here are some practice problems to help you distinguish between rational and irrational numbers:
1. Determine if the following numbers are rational or irrational:
a) √5
b) 1.25
c) π
d) 0.333333...
e) -⅝
2. Convert the following irrational numbers into decimal form, rounded to two decimal places:
a) √2
b) √3
c) √10
d) √13
e) √20
3. Simplify each of the following expressions:
a) √16
b) 4 - √9
c) √64 + √25
d) √(9/4)
e) 3√27
4. Determine if the following numbers are rational or irrational:
a) 0.999999999999999...
b) -√25
c) 6.75
d) ∛8
e) 2/3
Answers:
1.
a) Irrational
b) Rational
c) Irrational
d) Rational (repeating decimal)
e) Rational
2.
a) 1.41
b) 1.73
c) 3.16
d) 3.61
e) 4.47
3.
a) 4
b) 1
c) 14
d) 1.5
e) 9
4.
a) Rational (repeating decimal)
b) Irrational
c) Rational
d) Irrational
e) Rational
Make sure to practice more and solve similar problems to further strengthen your understanding of rational and irrational numbers.