Radicals
What is the square root of 49?
(Answer: √(49) = 7)
What is 2³?
(Answer: 8)
Is 1/2 a rational number? Why or why not?
(Answer: Yes, because it can be expressed as a fraction)
Provide an example of an irrational number.
(Answer: √3 or π)
What is the approximate value of √2 to two decimal places?
(Answer: 1.41)
Find the value of √(25) + √(4).
(Answer: 5 + 2 = 7)
Simplify the expression 5² × 5³.
(Answer: 5⁵ = 3125)
Give an example of a rational number between 1 and 2.
(Answer: 3/2 or 1.5)
Why is the square root of 2 considered an irrational number?
(Answer: It cannot be expressed as a fraction of two integers)
How could you use a rational number to approximate π?
(Answer: Use 22/7)
What is the value of √(16 × 9)?
(Answer: 12)
What does the expression x⁵ ÷ x² equal?
(Answer: x³)
What are the decimal representations of 3/4 and 1/5?
(Answer: 0.75 and 0.2)
How does π (pi) classify as an irrational number?
(Answer: It cannot be expressed as a fraction of two integers)
Why might one want to approximate an irrational number?
(Answer: To make calculations easier)
Simplify √36 + √64.
(Answer: 6 + 8 = 14)
If 3⁴ = 81, what is 3²?
(Answer: 9)
Explain how to determine if a number is rational.
(Answer: A number is rational if it can be expressed as a fraction a/b where a and b are integers and b ≠ 0)
Explain what makes an irrational number different from a rational number.
(Answer: Irrational numbers cannot be expressed as a fraction of two
If 1.414 is an approximation for √2, what are two rational numbers that are close to it?
(Answer: 1.4 and 1.41)
What is the square root of 49?
(Answer: 7)
Explain what it means to have a negative exponent, using 2⁻² as an example.
(Answer: 2⁻² = 1/2² = 1/4)
What is the sum of 2/3 and 1/4?
(Answer: 11/12)
What is an example of an operation that results in an irrational number?
(Answer: √2 + √3)
Explain how to approximate the square root of 10 using rational numbers.
(Answer: Between 3 and 4, closer to 3.16)