Rational or Irrational Numbers
Is ¾ a rational or irrational number?
Rational
Which is greater: 2 or √3?
2 is greater – √3 ≈ 1.73
What is the square root of 36?
6
What is the formula for the Pythagorean Theorem?
a² + b² = c²
Is 0.5 rational or irrational? Why?
Rational – it can be written as ½.
Is √16 a rational or irrational number?
Rational √16 = 4
Plot √4 on a number line. What number is it?
2
What is the cube root of 64?
4
a² + b² = c²
If a = 3 and b = 4, what is c?
5 – √(3² + 4²) = √(9 + 16) = √25 = 5
Convert ⅛ into a decimal.
0.125
Is √2 a rational or irrational number?
Irrational – it cannot be written as a fraction and its decimal never ends or repeats
Which is closer to 5: √26 or √27?
√26 – √26 ≈ 5.10, √27 ≈ 5.20
Is 7 a perfect square? Why or why not?
No – there is no whole number that multiplies to 7.
Is this a right triangle: 5, 12, 13? Use the converse.
Yes – 5² + 12² = 25 + 144 = 169 = 13²
Is 0.333… rational? Explain.
Yes – repeating decimals are rational.
Is π a rational or irrational number?
Irrational – it never ends and never repeats.
Place √10 on a number line between two whole numbers.
Between 3 and 4 – √10 ≈ 3.16
What is the volume of a cube with an edge length of 3?
27 – 3 × 3 × 3
Find the missing side: a = 6, c = 10. What is b?
8 – b² = 10² - 6² = 100 - 36 = 64 → b = √64 = 8
What kind of decimal never ends and never repeats?
Irrational decimal
Is 0.121212... rational or irrational? Explain why.
Rational – it’s a repeating decimal, and can be written as a fraction.
Which number is between √8 and √9 on the number line?
Any number between 2.83 and 3 – example: 2.9
If a cube has a volume of 125, what is the edge length?
5 – ∛125 = 5
A triangle has sides 7, 24, and 25. Is it a right triangle?
Yes – 7² + 24² = 49 + 576 = 625 = 25²
Explain why 0.727272... is a rational number.
It repeats and can be written as a fraction (8/11).