Question

simplify:
\frac{\sqrt{180} - 6}{18}
\bigcirc \frac{\sqrt{5} - 1}{3}
\bigcirc \sqrt{10} - 3
\bigcirc \frac{\sqrt{10} - 1}{3}
\bigcirc \frac{\sqrt{5} - 6}{3}

question 31

simplify the square root:
\sqrt{-384}
\bigcirc 24i\sqrt{4}
\bigcirc 4i\sqrt{24}
\bigcirc 8i\sqrt{6}
\bigcirc 6i\sqrt{8}

Explanation:

First Problem: Simplify $\frac{\sqrt{180}-6}{18}$

Step1: Simplify $\sqrt{180}$

$\sqrt{180} = \sqrt{36 \times 5} = 6\sqrt{5}$

Step2: Substitute into numerator

$6\sqrt{5} - 6 = 6(\sqrt{5} - 1)$

Step3: Divide by denominator

$\frac{6(\sqrt{5} - 1)}{18} = \frac{\sqrt{5} - 1}{3}$

Step1: Factor out -1 and simplify root

$\sqrt{-384} = \sqrt{-1 \times 64 \times 6} = \sqrt{-1} \times \sqrt{64} \times \sqrt{6}$

Step2: Substitute $i = \sqrt{-1}$

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

Answer:

$\frac{\sqrt{5}-1}{3}$

---

Second Problem: Simplify $\sqrt{-384}$