Find the two square roots of each number. If the number is not a EXERCISES perfect square, approximate the values to one decimal place. (Lesson 1.1) 1. 16 $$ \qquad $$ 2. $$ \frac{4}{25} $$ $$ \qquad $$ 3. 225 $$ \qquad $$ 4. $$ \frac{1}{49} $$ $$ \qquad $$ 5. $$ \sqrt{10} $$ $$ \qquad $$ 6. $$ \sqrt{18} $$ $$ \qquad $$ Write each decimal as a fraction in simplest form. (Lesson 1.1) 7. $$ 0 . \overline{5} $$ $$ \qquad $$ 8. $$ 0 . \overline{63} $$ $$ \qquad $$ 9. $$ 0 . \overline{214} $$ $$ \qquad $$ Solve each equation for $$ x $$. (Lesson 1.1) 10. $$ x^{2}=361 $$ 11. $$ x^{3}=1728 $$ 12. $$ x^{2}=\frac{49}{121} $$ $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ Write all names that apply to each number. (Lesson 1.2) 13. $$ \frac{2}{3} $$ 14. $$ -\sqrt{100} $$ $$ \qquad $$ $$ \qquad $$ 15. $$ \frac{15}{5} $$ 16. $$ \sqrt{21} $$ $$ \qquad $$ $$ \qquad $$ Compare. Write $$ $$, or $$ = $$. (Lesson 1.3) 17. $$ \sqrt{7}+5 $$ $$ 7+\sqrt{5} $$ 18. $$ 6+\sqrt{8} $$ $$ \sqrt{6}+8 $$ 19. $$ \sqrt{4}-2 $$ $$ 4-\sqrt{2} $$ Order the numbers from least to greatest. (Lesson 1.3) 20. $$ \sqrt{81}, \frac{72}{7}, 8.9 $$ $$ \qquad $$ 21. $$ \sqrt{7}, 2.55, \frac{7}{3} $$ $$ \qquad $$

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Find the two square roots of each number. If the number is not a EXERCISES perfect square, approximate the values to one decimal place. (Lesson 1.1) 1. 16 $$ \qquad $$ 2. $$ \frac{4}{25} $$ $$ \qquad $$ 3. 225 $$ \qquad $$ 4. $$ \frac{1}{49} $$ $$ \qquad $$ 5. $$ \sqrt{10} $$ $$ \qquad $$ 6. $$ \sqrt{18} $$ $$ \qquad $$ Write each decimal as a fraction in simplest form. (Lesson 1.1) 7. $$ 0 . \overline{5} $$ $$ \qquad $$ 8. $$ 0 . \overline{63} $$ $$ \qquad $$ 9. $$ 0 . \overline{214} $$ $$ \qquad $$ Solve each equation for $$ x $$. (Lesson 1.1) 10. $$ x^{2}=361 $$ 11. $$ x^{3}=1728 $$ 12. $$ x^{2}=\frac{49}{121} $$ $$ \qquad $$ $$ \qquad $$ $$ \qquad $$ Write all names that apply to each number. (Lesson 1.2) 13. $$ \frac{2}{3} $$ 14. $$ -\sqrt{100} $$ $$ \qquad $$ $$ \qquad $$ 15. $$ \frac{15}{5} $$ 16. $$ \sqrt{21} $$ $$ \qquad $$ $$ \qquad $$ Compare. Write $$ <_{1}> $$, or $$ = $$. (Lesson 1.3) 17. $$ \sqrt{7}+5 $$ $$ 7+\sqrt{5} $$ 18. $$ 6+\sqrt{8} $$ $$ \sqrt{6}+8 $$ 19. $$ \sqrt{4}-2 $$ $$ 4-\sqrt{2} $$ Order the numbers from least to greatest. (Lesson 1.3) 20. $$ \sqrt{81}, \frac{72}{7}, 8.9 $$ $$ \qquad $$ 21. $$ \sqrt{7}, 2.55, \frac{7}{3} $$ $$ \qquad $$

UpStudy AI · Accepted Answer

To find the square roots of each number, we will use the square root function.

1. For 16:
   - The square root of 16 is 4.

2. For $$ \frac{4}{25} $$:
   - The square root of $$ \frac{4}{25} $$ is $$ \frac{2}{5} $$.

3. For 225:
   - The square root of 225 is 15.

4. For $$ \frac{1}{49} $$:
   - The square root of $$ \frac{1}{49} $$ is $$ \frac{1}{7} $$.

5. For $$ \sqrt{10} $$:
   - The square root of 10 is approximately 3.162.

6. For $$ \sqrt{18} $$:
   - The square root of 18 is approximately 4.243.

Now, let's move on to the next set of questions.
1. $$ \sqrt{16} = 4 $$ 2. $$ \sqrt{\frac{4}{25}} = \frac{2}{5} $$ 3. $$ \sqrt{225} = 15 $$ 4. $$ \sqrt{\frac{1}{49}} = \frac{1}{7} $$ 5. $$ \sqrt{10} \approx 3.162 $$ 6. $$ \sqrt{18} \approx 4.243 $$ 7. $$ 0.\overline{5} = \frac{5}{9} $$ 8. $$ 0.\overline{63} = \frac{63}{99} = \frac{21}{33} = \frac{7}{11} $$ 9. $$ 0.\overline{214} = \frac{214}{999} $$ 10. $$ x^2 = 361 $$ - $$ x = \sqrt{361} = 19 $$ or $$ x = -19 $$ 11. $$ x^3 = 1728 $$ - $$ x = \sqrt[3]{1728} = 12 $$ 12. $$ x^2 = \frac{49}{121} $$ - $$ x = \sqrt{\frac{49}{121}} = \frac{7}{11} $$ or $$ x = -\frac{7}{11} $$ 13. $$ \frac{2}{3} $$ is a **rational number**, **proper fraction**, and **terminating decimal**. 14. $$ -\sqrt{100} = -10 $$ is a **rational number**, **integer**, and **whole number**. 15. $$ \frac{15}{5} = 3 $$ is a **rational number**, **integer**, and **whole number**. 16. $$ \sqrt{21} $$ is an **irrational number**, **real number**, and **positive number**. 17. $$ \sqrt{7} + 5 $$ vs. $$ 7 + \sqrt{5} $$ - $$ \sqrt{7} \approx 2.6458 $$ - $$ \sqrt{5} \approx 2.2361 $$ - $$ \sqrt{7} + 5 \approx 7.6458 $$ - $$ 7 + \sqrt{5} \approx 9.2361 $$ - Therefore, $$ \sqrt{7} + 5 < 7 + \sqrt{5} $$ 18. $$ 6 + \sqrt{8} $$ vs. $$ \sqrt{6} + 8 $$ - $$ \sqrt{8} \approx 2.8284 $$ - $$ \sqrt{6} \approx 2.4495 $$ - $$ 6 + \sqrt{8} \approx 8.8284 $$ - $$ \sqrt{6} + 8 \approx 10.4495 $$ - Therefore, $$ 6 + \sqrt{8} < \sqrt{6} + 8 $$ 19. $$ \sqrt{4} - 2 $$ vs. $$ 4 - \sqrt{2} $$ - $$ \sqrt{4} = 2 $$ - $$ \sqrt{2} \approx 1.4142 $$ - $$ \sqrt{4} - 2 = 0 $$ - $$ 4 - \sqrt{2} \approx 2.5858 $$ - Therefore, $$ \sqrt{4} - 2 < 4 - \sqrt{2} $$ 20. $$ \sqrt{81}, \frac{72}{7}, 8.9 $$ - $$ \sqrt{81} = 9 $$ - $$ \frac{72}{7} \approx 10.2857 $$ - $$ 8.9 $$ - Therefore, the order from least to greatest is: $$ 8.9, \sqrt{81}, \frac{72}{7} $$ 21. $$ \sqrt{7}, 2.55, \frac{7}{3} $$ - $$ \sqrt{7} \approx 2.6458 $$ - $$ \frac{7}{3} \approx 2.3333 $$ - $$ 2.55 $$ - Therefore, the order from least to greatest is: $$ \frac{7}{3}, \sqrt{7}, 2.55 $$

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