Unit 2 • Lessons 4–5 (Operations on Radicals) — Quiz
Dividing radicals • Rationalizing monomial & binomial denominators • Conjugates
Divide Radicals
Rationalize Monomial
Rationalize Binomial (Conjugate)
Practice Set
Each question allows 2 attempts. Use the whiteboard under each problem, then click Reveal Solution if needed.
1) Divide Radicals
Simplify \(\dfrac{\sqrt{50}}{\sqrt{2}}\).
\(\dfrac{\sqrt{50}}{\sqrt{2}}=\sqrt{\dfrac{50}{2}}=\sqrt{25}=5.\)
2) Divide & Simplify
Simplify \(\dfrac{\sqrt{48}}{2\sqrt{3}}\).
\(\sqrt{48}=4\sqrt{3}\Rightarrow \dfrac{4\sqrt{3}}{2\sqrt{3}}=2.\)
3) Rationalize a Monomial Denominator
Rationalize: \(\dfrac{7}{\sqrt{5}}\).
Multiply by \(\frac{\sqrt{5}}{\sqrt{5}}\): \(\dfrac{7\sqrt{5}}{5}\).
4) Rationalize a Monomial Denominator
Rationalize: \(\dfrac{3}{2\sqrt{7}}\).
Multiply by \(\frac{\sqrt{7}}{\sqrt{7}}\): \(\dfrac{3\sqrt{7}}{2\cdot 7}=\dfrac{3\sqrt{7}}{14}\).
5) Divide & Simplify
Simplify \(\dfrac{5\sqrt{6}}{\sqrt{3}}\).
\(\dfrac{5\sqrt{6}}{\sqrt{3}}=5\sqrt{2}\) (since \(\sqrt{6}/\sqrt{3}=\sqrt{2}\)).
6) Rationalize a Binomial Denominator (Conjugate)
Rationalize: \(\dfrac{4}{\sqrt{3}+\sqrt{2}}\).
Multiply by conjugate \(\dfrac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}\): denominator \(=3-2=1\Rightarrow 4(\sqrt{3}-\sqrt{2}).\)
7) Divide Expression
Simplify \(\dfrac{2\sqrt{5}+\sqrt{20}}{\sqrt{5}}\).
\(\sqrt{20}=2\sqrt{5}\Rightarrow \dfrac{2\sqrt{5}+2\sqrt{5}}{\sqrt{5}}=\dfrac{4\sqrt{5}}{\sqrt{5}}=4.\)
8) Rationalize a Binomial Denominator
Rationalize: \(\dfrac{5}{\sqrt{8}-\sqrt{2}}\).
Multiply by \(\dfrac{\sqrt{8}+\sqrt{2}}{\sqrt{8}+\sqrt{2}}\): denominator \(=8-2=6\).
Numerator \(=5(\sqrt{8}+\sqrt{2})=5(2\sqrt{2}+\sqrt{2})=15\sqrt{2}\).
Result \(\dfrac{15\sqrt{2}}{6}=\dfrac{5\sqrt{2}}{2}\).
Progress
Score: 0/8