Question

multiply / divide radical expressions
score: 5/7 penalty: none
question
express in simplest radical form.
\\(\frac{\sqrt{2000}}{\sqrt{8}}\\)

Explanation:

Step1: Use quotient rule for radicals

The quotient rule for radicals states that $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$ (where $a\geq0$ and $b > 0$). So we can rewrite $\frac{\sqrt{2000}}{\sqrt{8}}$ as $\sqrt{\frac{2000}{8}}$.

Step2: Simplify the fraction inside the radical

Calculate $\frac{2000}{8}=250$. So now we have $\sqrt{250}$.

Step3: Factor the radicand into a perfect square and another number

Factor 250 as $25\times10$, where 25 is a perfect square. So $\sqrt{250}=\sqrt{25\times10}$.

Step4: Use product rule for radicals

The product rule for radicals states that $\sqrt{ab}=\sqrt{a}\times\sqrt{b}$ (where $a\geq0$ and $b\geq0$). So $\sqrt{25\times10}=\sqrt{25}\times\sqrt{10}$.

Step5: Simplify $\sqrt{25}$

Since $5^2 = 25$, $\sqrt{25}=5$. So we get $5\sqrt{10}$.

Answer:

$5\sqrt{10}$