1.02 Rational and irrational numbers
Classify the following numbers as rational or irrational:
Is \sqrt{15} an integer?
Classify the following numbers as rational or irrational:
\sqrt{7}
\left(\sqrt{7}\right)^{2}
\sqrt{35}
\sqrt{81}
\sqrt{23}
\sqrt{64}
Simplify each of the following numbers and state whether they are rational or irrational:
\sqrt{16}
\dfrac{2\pi}{8}
-\dfrac{4\pi}{5\pi}
\dfrac{0.4}{5}
Akin states that 24.737337333... is a rational number because it has a repeating pattern.
Is Akin correct? Explain your answer.
Plot the following numbers on the following number line:
-3
\pi
0.5
\sqrt{3}
\dfrac{4}{5}
-2.2
\sqrt{7}
-\dfrac{3}{2}
Plot the following sets of numbers on a number line:
2, \, \dfrac{5}{2}, \, \pi
-2, \, -\dfrac{1}{2}, \, \sqrt{3}
3, \, -2.3, \, \sqrt{5}
1.7, \, -1.1, \, \dfrac{7}{3}
Plot the following surds on a number line:
State the integer that each of the following numbers is closest in value to:
Which one of the following has a value between 10 and 11?
Consider the number \sqrt{22}.
Complete the inequality with two consecutive perfect square numbers that 22 lies between:⬚ < 22 < ⬚
Complete the inequality with two consecutive integers that \sqrt{22} lies between:⬚ < \sqrt{22} < ⬚
Consider the number \sqrt{59}.
Complete the inequality with two consecutive perfect square numbers that 59 lies between:⬚ < 59 < ⬚
Complete the inequality with two consecutive integers that \sqrt{59} lies between:⬚ < \sqrt{59} < ⬚
Determine the two consecutive integers that will complete the following inequalities:
State the integer that lies between \sqrt{12} and \sqrt{22}.
For each of the following pairs of numbers, select the number with the larger value:
\sqrt{27} or \sqrt{22}
\sqrt{50} or \sqrt{46}
\sqrt{20} or 5
\sqrt{15} or 3
For each of the following pairs of numbers, select the number with the smaller value:
4 \pi or 12
\pi^2 or 144
\sqrt{120} or 11
\sqrt{72} or 8