Question

1
rewrite each radical expression in simplest form.
a) \\(\sqrt{27}\\)
b) \\(2\sqrt{90}\\)
2
rewrite each radical expression in simplest form.
a) \\(4\sqrt{162}\\)
b) \\(\sqrt{320}\\)

Explanation:

Step1: Factor out perfect square (1a)

$\sqrt{27} = \sqrt{9 \times 3}$

Step2: Simplify perfect square root (1a)

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

Step3: Factor out perfect square (1b)

$2\sqrt{90} = 2\sqrt{9 \times 10}$

Step4: Simplify perfect square root (1b)

$2\sqrt{9 \times 10} = 2 \times \sqrt{9} \times \sqrt{10} = 2 \times 3\sqrt{10} = 6\sqrt{10}$

Step5: Factor out perfect square (2a)

$4\sqrt{162} = 4\sqrt{81 \times 2}$

Step6: Simplify perfect square root (2a)

$4\sqrt{81 \times 2} = 4 \times \sqrt{81} \times \sqrt{2} = 4 \times 9\sqrt{2} = 36\sqrt{2}$

Step7: Factor out perfect square (2b)

$\sqrt{320} = \sqrt{64 \times 5}$

Step8: Simplify perfect square root (2b)

$\sqrt{64 \times 5} = \sqrt{64} \times \sqrt{5} = 8\sqrt{5}$

Answer:

1a) $3\sqrt{3}$
1b) $6\sqrt{10}$
2a) $36\sqrt{2}$
2b) $8\sqrt{5}$