Question

identify the following as rational or irrational numbers. if they are rational, write them as simplified fractions.

1. \\(\sqrt{400}\\) 17. \\(\sqrt{56}\\) 18. \\(\sqrt{196}\\)
2. \\(\sqrt{1000}\\) 20. \\(\sqrt{125}\\) 21. \\(\sqrt{1}\\)

give the decimal approximation of the radicals to the nearest tenths place

1. \\(\sqrt{18}\\) 23. \\(\sqrt{72}\\)
2. \\(\sqrt{130}\\) 25. \\(\sqrt{156}\\)

Explanation:

Step1: Evaluate $\sqrt{400}$

$\sqrt{400} = 20 = \frac{20}{1}$ (rational)

Step2: Evaluate $\sqrt{56}$

$\sqrt{56} = \sqrt{4 \times 14} = 2\sqrt{14}$ (irrational, $\sqrt{14}$ is non-terminating/non-repeating)

Step3: Evaluate $\sqrt{196}$

$\sqrt{196} = 14 = \frac{14}{1}$ (rational)

Step4: Evaluate $\sqrt{1000}$

$\sqrt{1000} = \sqrt{100 \times 10} = 10\sqrt{10}$ (irrational, $\sqrt{10}$ is non-terminating/non-repeating)

Step5: Evaluate $\sqrt{125}$

$\sqrt{125} = \sqrt{25 \times 5} = 5\sqrt{5}$ (irrational, $\sqrt{5}$ is non-terminating/non-repeating)

Step6: Evaluate $\sqrt{1}$

$\sqrt{1} = 1 = \frac{1}{1}$ (rational)

Step7: Approximate $\sqrt{18}$ to tenths

$\sqrt{18} \approx 4.2426 \approx 4.2$

Step8: Approximate $\sqrt{72}$ to tenths

$\sqrt{72} = 6\sqrt{2} \approx 8.4853 \approx 8.5$

Step9: Approximate $\sqrt{130}$ to tenths

$\sqrt{130} \approx 11.4018 \approx 11.4$

Step10: Approximate $\sqrt{156}$ to tenths

$\sqrt{156} \approx 12.4900 \approx 12.5$

Answer:

1. Rational, $\frac{20}{1}$
2. Irrational
3. Rational, $\frac{14}{1}$
4. Irrational
5. Irrational
6. Rational, $\frac{1}{1}$
7. $4.2$
8. $8.5$
9. $11.4$
10. $12.5$