Answer
(a) $2~\sqrt{2}$
(b) $3~\sqrt{5}$
(c) $30$
(d) $3$
Work Step by Step
We can simplify the following expressions:
(a) $\sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2~\sqrt{2}$
(b) $\sqrt{45} = \sqrt{9 \cdot 5} = \sqrt{9} \cdot \sqrt{5} = 3~\sqrt{5}$
(c) $\sqrt{900} = \sqrt{9 \cdot 100} = \sqrt{9} \cdot \sqrt{100} = (3)(10) = 30$
(d) $(\sqrt{3})^2 = \sqrt{3} \cdot \sqrt{3} = \sqrt{3 \cdot 3} = \sqrt{9} = 3$
