Question

name: ____ date: __ bell: ____ galindo algebra 1b simplifying non - perfect radicals simplify the following square and cube roots. show work! 13. \\(\sqrt{112}\\) 14. \\(\sqrt{20}\\) 15. \\(\sqrt{128}\\) 16. \\(\sqrt{288}\\) 17. \\(\sqrt{384}\\) 18. \\(\sqrt{75}\\) 19. \\(\sqrt{54}\\) 20. \\(\sqrt{243}\\) 21. \\(\sqrt{12}\\) 22. \\(\sqrt{405}\\) 23. \\(\sqrt{80}\\) 24. \\(\sqrt{600}\\) 25. \\(\sqrt3{56}\\) 26. \\(\sqrt3{-128}\\) 27. \\(\sqrt3{192}\\) 28. \\(\sqrt3{375}\\) 29. \\(\sqrt3{-250}\\) 30. \\(\sqrt3{135}\\)

Explanation:

Step1: Factor out perfect square

$\sqrt{112} = \sqrt{16 \times 7}$

Step2: Simplify perfect square root

$\sqrt{16 \times 7} = \sqrt{16} \times \sqrt{7} = 4\sqrt{7}$

Step1: Factor out perfect square

$\sqrt{20} = \sqrt{4 \times 5}$

Step2: Simplify perfect square root

$\sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}$

Step1: Factor out perfect square

$\sqrt{128} = \sqrt{64 \times 2}$

Step2: Simplify perfect square root

$\sqrt{64 \times 2} = \sqrt{64} \times \sqrt{2} = 8\sqrt{2}$

Step1: Factor out perfect square

$\sqrt{288} = \sqrt{144 \times 2}$

Step2: Simplify perfect square root

$\sqrt{144 \times 2} = \sqrt{144} \times \sqrt{2} = 12\sqrt{2}$

Step1: Factor out perfect square

$\sqrt{384} = \sqrt{64 \times 6}$

Step2: Simplify perfect square root

$\sqrt{64 \times 6} = \sqrt{64} \times \sqrt{6} = 8\sqrt{6}$

Step1: Factor out perfect square

$\sqrt{75} = \sqrt{25 \times 3}$

Step2: Simplify perfect square root

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

Step1: Factor out perfect square

$\sqrt{54} = \sqrt{9 \times 6}$

Step2: Simplify perfect square root

$\sqrt{9 \times 6} = \sqrt{9} \times \sqrt{6} = 3\sqrt{6}$

Step1: Factor out perfect square

$\sqrt{243} = \sqrt{81 \times 3}$

Step2: Simplify perfect square root

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

Step1: Factor out perfect square

$\sqrt{12} = \sqrt{4 \times 3}$

Step2: Simplify perfect square root

$\sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}$

Step1: Factor out perfect square

$\sqrt{405} = \sqrt{81 \times 5}$

Step2: Simplify perfect square root

$\sqrt{81 \times 5} = \sqrt{81} \times \sqrt{5} = 9\sqrt{5}$

Step1: Factor out perfect square

$\sqrt{80} = \sqrt{16 \times 5}$

Step2: Simplify perfect square root

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

Step1: Factor out perfect square

$\sqrt{600} = \sqrt{100 \times 6}$

Step2: Simplify perfect square root

$\sqrt{100 \times 6} = \sqrt{100} \times \sqrt{6} = 10\sqrt{6}$

Step1: Factor out perfect cube

$\sqrt[3]{56} = \sqrt[3]{8 \times 7}$

Step2: Simplify perfect cube root

$\sqrt[3]{8 \times 7} = \sqrt[3]{8} \times \sqrt[3]{7} = 2\sqrt[3]{7}$

Step1: Factor out perfect cube

$\sqrt[3]{-128} = \sqrt[3]{-64 \times 2}$

Step2: Simplify perfect cube root

$\sqrt[3]{-64 \times 2} = \sqrt[3]{-64} \times \sqrt[3]{2} = -4\sqrt[3]{2}$

Step1: Factor out perfect cube

$\sqrt[3]{192} = \sqrt[3]{64 \times 3}$

Step2: Simplify perfect cube root

$\sqrt[3]{64 \times 3} = \sqrt[3]{64} \times \sqrt[3]{3} = 4\sqrt[3]{3}$

Step1: Factor out perfect cube

$\sqrt[3]{375} = \sqrt[3]{125 \times 3}$

Step2: Simplify perfect cube root

$\sqrt[3]{125 \times 3} = \sqrt[3]{125} \times \sqrt[3]{3} = 5\sqrt[3]{3}$

Step1: Factor out perfect cube

$\sqrt[3]{-250} = \sqrt[3]{-125 \times 2}$

Step2: Simplify perfect cube root

$\sqrt[3]{-125 \times 2} = \sqrt[3]{-125} \times \sqrt[3]{2} = -5\sqrt[3]{2}$

Step1: Factor out perfect cube

$\sqrt[3]{135} = \sqrt[3]{27 \times 5}$

Step2: Simplify perfect cube root

$\sqrt[3]{27 \times 5} = \sqrt[3]{27} \times \sqrt[3]{5} = 3\sqrt[3]{5}$

Answer:

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