Question

8.5 divide radical expressions (homework)
score: 0/14 answered: 0/14
question 1
simplify.
\\(\frac{\sqrt{1000}}{\sqrt{30}}=\\)

Explanation:

Step1: Use quotient - rule of radicals

The quotient - rule of radicals states that $\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}$ for $a\geq0$ and $b > 0$. So, $\frac{\sqrt{1000}}{\sqrt{30}}=\sqrt{\frac{1000}{30}}$.

Step2: Simplify the fraction inside the radical

$\frac{1000}{30}=\frac{100}{3}$ after dividing both the numerator and denominator by 10. So we have $\sqrt{\frac{100}{3}}$.

Step3: Use the property $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$

$\sqrt{\frac{100}{3}}=\frac{\sqrt{100}}{\sqrt{3}}$. Since $\sqrt{100} = 10$, the expression becomes $\frac{10}{\sqrt{3}}$.

Step4: Rationalize the denominator

Multiply the numerator and denominator by $\sqrt{3}$. We get $\frac{10\sqrt{3}}{3}$.

Answer:

$\frac{10\sqrt{3}}{3}$