Question

simplify.

1. \\(\sqrt{200}\\)
2. \\(\sqrt{80}\\)
3. \\(\sqrt{162}\\)
4. \\(\sqrt{75}\\)
5. \\(\sqrt{180}\\)
6. \\(\sqrt{490}\\)
7. \\(\sqrt{192}\\)
8. \\(\sqrt{225}\\)
9. \\(\sqrt{63}\\)
10. \\(\sqrt{72}\\)
11. \\(\sqrt{245}\\)
12. \\(\sqrt{125}\\)
13. \\(\sqrt{112}\\)
14. \\(\sqrt{243}\\)
15. \\(\sqrt{810}\\)
16. \\(\sqrt{98}\\)
17. \\(\sqrt{384}\\)
18. \\(\sqrt{28}\\)
19. \\(\sqrt{20}\\)
20. \\(\sqrt{48}\\)

Explanation:

Step1: Factor out perfect square

For each square root, rewrite the radicand as a product of the largest perfect square factor and a remaining factor, then use the property $\sqrt{ab}=\sqrt{a}\sqrt{b}$ where $a$ is a perfect square.
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2) $\sqrt{80}$

Step1: Factor into perfect square

$\sqrt{16 \times 5}$

Step2: Split and simplify

$\sqrt{16}\sqrt{5} = 4\sqrt{5}$

4) $\sqrt{75}$

Step1: Factor into perfect square

$\sqrt{25 \times 3}$

Step2: Split and simplify

$\sqrt{25}\sqrt{3} = 5\sqrt{3}$

6) $\sqrt{490}$

Step1: Factor into perfect square

$\sqrt{49 \times 10}$

Step2: Split and simplify

$\sqrt{49}\sqrt{10} = 7\sqrt{10}$

8) $\sqrt{225}$

Step1: Identify perfect square

$\sqrt{15^2}$

Step2: Simplify square root

$15$

10) $\sqrt{72}$

Step1: Factor into perfect square

$\sqrt{36 \times 2}$

Step2: Split and simplify

$\sqrt{36}\sqrt{2} = 6\sqrt{2}$

12) $\sqrt{125}$

Step1: Factor into perfect square

$\sqrt{25 \times 5}$

Step2: Split and simplify

$\sqrt{25}\sqrt{5} = 5\sqrt{5}$

14) $\sqrt{243}$

Step1: Factor into perfect square

$\sqrt{81 \times 3}$

Step2: Split and simplify

$\sqrt{81}\sqrt{3} = 9\sqrt{3}$

16) $\sqrt{98}$

Step1: Factor into perfect square

$\sqrt{49 \times 2}$

Step2: Split and simplify

$\sqrt{49}\sqrt{2} = 7\sqrt{2}$

18) $\sqrt{28}$

Step1: Factor into perfect square

$\sqrt{4 \times 7}$

Step2: Split and simplify

$\sqrt{4}\sqrt{7} = 2\sqrt{7}$

20) $\sqrt{48}$

Step1: Factor into perfect square

$\sqrt{16 \times 3}$

Step2: Split and simplify

$\sqrt{16}\sqrt{3} = 4\sqrt{3}$
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Answer:

1. $10\sqrt{2}$
2. $4\sqrt{5}$
3. $9\sqrt{2}$
4. $5\sqrt{3}$
5. $6\sqrt{5}$
6. $7\sqrt{10}$
7. $8\sqrt{3}$
8. $15$
9. $3\sqrt{7}$
10. $6\sqrt{2}$
11. $7\sqrt{5}$
12. $5\sqrt{5}$
13. $4\sqrt{7}$
14. $9\sqrt{3}$
15. $9\sqrt{10}$
16. $7\sqrt{2}$
17. $8\sqrt{6}$
18. $2\sqrt{7}$
19. $2\sqrt{5}$
20. $4\sqrt{3}$