Simplify the following. Express your answer in simplest radical form.
- \( \displaystyle \sqrt[4]{48} \)
Solution
\( \displaystyle 2\sqrt[4]{3} \)
- \( \displaystyle \sqrt{75x^3} \)
Solution
\( \displaystyle 5x\sqrt{3x}\)
- \( \displaystyle \sqrt[4]{\left(5x\right)^4} \)
Solution
\( \displaystyle 5|x|\)
- \( \displaystyle \sqrt[3]{24} \)
Solution
\( \displaystyle 2\sqrt[3]{3}\)
- \( \displaystyle \sqrt[3]{24a^4} \)
Solution
\( \displaystyle 2a\sqrt[3]{3a}\)
- \( \displaystyle \sqrt[3]{-40x^6} \)
Solution
\( \displaystyle -2x^2 \sqrt[3]{5} \)
- \( \displaystyle \frac{\sqrt{8}}{2} \)
Solution
\( \displaystyle \sqrt{2}\)
- \( \displaystyle \frac{\sqrt{5} + \sqrt{3}}{\sqrt{3}} \)
Solution
\( \displaystyle \frac{\sqrt{15} + 3}{3} \)
- \( \displaystyle \frac{\sqrt{12} - 3}{\sqrt{8}} \)
Solution
\( \displaystyle \frac{2\sqrt{6} - 3\sqrt{2}}{4} \)
- \( \displaystyle \sqrt{\sqrt[4]{2x}} \)
Solution
\( \displaystyle \sqrt[8]{2x} \)
- \( \displaystyle \sqrt[5]{\sqrt[3]{10a^8b^{15}}} \)
Solution
\( \displaystyle b\sqrt[15]{10a^8} \)
- \( \displaystyle \sqrt[3]{\frac{5}{4y^2}} \)
Solution
\( \displaystyle \frac{\sqrt[3]{10y}}{2y} \)
- \( \displaystyle \frac{6a^2}{\sqrt[4]{8a^2}} \)
Solution
\( \displaystyle 3|a|\sqrt[4]{2a^2} \)
- \( \displaystyle \frac{12n}{\sqrt[3]{9n^7}} \)
Solution
\( \displaystyle \frac{4\sqrt[3]{3n^2}}{n^2} \)
- \( \displaystyle \frac{4}{\sqrt[3]{7} - \sqrt[3]{5}} \)
Solution
\( \displaystyle 2\sqrt[3]{49} + 2\sqrt[3]{35} + 2\sqrt[3]{25} \)
- \( \displaystyle \frac{-2}{\sqrt[3]{a} + 4} \)
Solution
\( \displaystyle \frac{-2\sqrt[3]{a^2} + 8\sqrt[3]{a} - 32}{a + 64} \)
- \( \displaystyle \sqrt[3]{x^{6n}} \)
Solution
\( \displaystyle x^{2n} \)
- \( \displaystyle \sqrt[4]{y^{4n + 12}} \)
Solution
\( \displaystyle \left| y^{n + 3}\right| \)
- \( \displaystyle \sqrt[3]{x^{2n + 1}} \cdot \sqrt[3]{x^{4n + 2}} \)
Solution
\( \displaystyle x^{2n + 1}\)
- \( \displaystyle y^n \cdot \sqrt[4]{y^{3n}} + \sqrt[4]{y^{7n}}, y > 0. \)
Solution
\( \displaystyle 2y^n\sqrt[4]{y^{3n}} \)
- \( \displaystyle \sqrt[n]{x^n} \)
Solution
\( x \) if \(n\) is odd; \( |x| \) if \(n\) is even
- \( \displaystyle \sqrt[n]{3^{3n + 2}} \)
Solution
\( \displaystyle 27 \sqrt[n]{9} \)
- \( \displaystyle \sqrt[n]{a^nx^{5n+1}} \) for \(a, x > 0\)
Solution
\( \displaystyle ax^5 \sqrt[n]{x} \) for \(a, x > 0\)
- \( \displaystyle \sqrt[n]{ab^{2n}x^{2n+3}} \) for \(a, x > 0\)
Solution
\( \displaystyle b^2x^2\sqrt[n]{ax^3} \) for \(a, x > 0\)