Notes
Problems & Videos
Simplify.
\(\textbf{1)}\) \( 2\sqrt[4]{3}+4\sqrt[4]{3} \)
The answer is \( 6\displaystyle\sqrt[4]{3} \)
\(\textbf{2)}\) \( \displaystyle\sqrt{30}+\displaystyle\sqrt{5} \)
The answer is \( \displaystyle\sqrt{30}+\displaystyle\sqrt{5} \)
\(\textbf{3)}\) \( \displaystyle\sqrt[3]{48} \)
The answer is \( 2\displaystyle\sqrt[3]{6} \)
\(\textbf{4)}\) \( 5\displaystyle\sqrt{3}-\displaystyle\sqrt{27} \)
The answer is \( 2\displaystyle\sqrt{3} \)
\(\textbf{5)}\) \( \displaystyle\sqrt{5}\cdot\displaystyle\sqrt{125} \)
The answer is \( 25 \)
\(\textbf{6)}\) \( (1-\displaystyle\sqrt{3})^{2} \)
The answer is \( 4-2\displaystyle\sqrt{3} \)
\(\textbf{7)}\) \( (\displaystyle\sqrt{18}+\displaystyle\sqrt{12})^{2} \)
The answer is \( 30+12\sqrt{6} \)
\(\textbf{8)}\) \( \displaystyle\sqrt{15}(2+\displaystyle\sqrt{3}) \)
The answer is \( 2\displaystyle\sqrt{15}+3\displaystyle\sqrt{5} \)
\(\textbf{9)}\) \( \displaystyle\frac{3\displaystyle\sqrt{10}}{4+\displaystyle\sqrt{2}} \)
The answer is \( \displaystyle\frac{6\displaystyle\sqrt{10}-3\displaystyle\sqrt{5}}{7} \)
\(\textbf{10)}\) \( \displaystyle\frac{5+6\displaystyle\sqrt{3}}{3-2\displaystyle\sqrt{3}} \)
The answer is \( -\displaystyle\frac{51+28\displaystyle\sqrt{3}}{3} \)
\(\textbf{11)}\) \( \displaystyle\frac{6-2\displaystyle\sqrt{2}}{\displaystyle\sqrt{2}} \)
The answer is \( 3\displaystyle\sqrt{2}-2 \)
\(\textbf{12)}\) \( (5\displaystyle\sqrt[3]{18})(3\displaystyle\sqrt[3]{6}) \)
The answer is \( 45\displaystyle\sqrt[3]{4} \)
\(\textbf{13)}\) \( \displaystyle\frac{6}{\displaystyle\sqrt[3]{5}} \)
The answer is \( \displaystyle\frac{6\displaystyle\sqrt[3]{25}}{5} \)
\(\textbf{14)}\) \( \displaystyle\sqrt[5]{64} \)
The answer is \( 2\displaystyle\sqrt[5]{2} \)
\(\textbf{15)}\) \( (\displaystyle\sqrt{8})(\displaystyle\sqrt{12})(\displaystyle\sqrt{3}) \)
The answer is \( 12\displaystyle\sqrt{2} \)
\(\textbf{16)}\) \( \displaystyle\frac{4}{5+\displaystyle\sqrt{3}} \)
The answer is \( \displaystyle\frac{10-2\displaystyle\sqrt{3}}{11} \)
\(\textbf{17)}\) \( \displaystyle\sqrt[3]{18}\cdot\displaystyle\sqrt[3]{12} \)
The answer is \( 6 \)
\(\textbf{18)}\) \( \displaystyle\frac{\displaystyle\sqrt[4]{48}}{\displaystyle\sqrt[4]{3}} \)
The answer is \( 2 \)
\(\textbf{19)}\) \( \displaystyle\sqrt[3]{40} \)
The answer is \( 2\displaystyle\sqrt[3]{5} \)
\(\,\,\,\,\,\displaystyle\sqrt[3]{40}\)
\(\,\,\,\,\,\displaystyle\sqrt[3]{2 \cdot 2 \cdot 2 \cdot 5}\)
\(\,\,\,\,\,\displaystyle\sqrt[3]{2 \cdot 2 \cdot 2}\sqrt[3]{5}\)
\(\,\,\,\,\,\displaystyle\sqrt[3]{8}\sqrt[3]{5}\)
\(\,\,\,\,\,\displaystyle2\sqrt[3]{5}\)
\(\textbf{20)}\) \( \displaystyle\frac{\displaystyle\sqrt[4]{3}}{\displaystyle\sqrt[4]{8}} \)
The answer is \( \displaystyle\frac{\displaystyle\sqrt[4]{6}}{2} \)
\(\textbf{21)}\) \( \left(3\sqrt{2}-4\sqrt{3}\right)\left(5\sqrt{6}+9\sqrt{12}\right) \)
The answer is \( 30\sqrt{3}+54\sqrt{6}-60\sqrt{2}-216 \)
\(\textbf{22)}\) \( \left(4+\sqrt{2}\right)\left(6-\sqrt{8}\right) \)
The answer is \( 20-2\sqrt{2} \)
\(\textbf{23)}\) \( \left(\sqrt{3}-1\right)\left(5+\sqrt{27}\right) \)
The answer is \( 2\sqrt{3}+4 \)
\(\textbf{24)}\) \( \left(2+\sqrt{2}\right)\left(8+\sqrt{8}\right) \)
The answer is \( 20+12\sqrt{2} \)
\(\textbf{25)}\) \( \displaystyle\frac{\sqrt{12}-4}{5+\sqrt{27}} \)
The answer is \( -11\sqrt{3}+19 \)
\(\textbf{26)}\) \( \displaystyle\frac{5\sqrt{6}-6}{2-\sqrt{6}} \)
The answer is \( -2\sqrt{6}-9 \)
\(\textbf{27)}\) \( \displaystyle\frac{\sqrt{6}-6}{2-\sqrt{6}} \)
The answer is \( 2\sqrt{6}+3 \)
\(\textbf{28)}\) Simplify \( \displaystyle\frac{2}{\sqrt[5]{8}} \)
The answer is \( \displaystyle\sqrt[5]{4} \)
\(\,\,\,\,\,\,\frac{2}{\sqrt[5]{8}}\)
\(\,\,\,\,\,\,\frac{2}{\sqrt[5]{2^3}}\)
\(\,\,\,\,\,\,\frac{2}{\sqrt[5]{2^3}}\cdot\frac{\sqrt[5]{2^2}}{\sqrt[5]{2^2}}\)
\(\,\,\,\,\,\,\frac{2\sqrt[5]{2^2}}{\sqrt[5]{2^5}}\)
\(\,\,\,\,\,\,\frac{2\sqrt[5]{4}}{2}\)
\(\,\,\,\,\,\,\sqrt[5]{4}\)
The answer is \(\sqrt[5]{4}\)
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