Question

8.5 divide radical expressions (homework) score: 8/14 answered: 8/14 question 9 rationalize the denominator: $\frac{sqrt{10}}{2 - sqrt{3}}=$ question help: video written example submit question jump to answer

Explanation:

Step1: Multiply by conjugate

Multiply numerator and denominator by $2 + \sqrt{3}$.
$\frac{\sqrt{10}(2+\sqrt{3})}{(2 - \sqrt{3})(2+\sqrt{3})}$

Step2: Expand denominator

Use $(a - b)(a + b)=a^{2}-b^{2}$. Here $a = 2$ and $b=\sqrt{3}$, so $(2 - \sqrt{3})(2+\sqrt{3})=2^{2}-(\sqrt{3})^{2}=4 - 3=1$.
The numerator is $\sqrt{10}(2+\sqrt{3})=2\sqrt{10}+\sqrt{30}$.

Step3: Simplify fraction

Since denominator is 1, the expression is $2\sqrt{10}+\sqrt{30}$.

Answer:

$2\sqrt{10}+\sqrt{30}$