Simplify \(0+\sqrt{3}\) to \(\sqrt{3}\).
\[\begin{aligned}&\frac{7\sqrt{3}}{\sqrt{\sqrt{3}}}-\frac{{2}^{\sqrt{5}}}{\sqrt{6}\sqrt{55}}\\&\frac{3\sqrt{2}}{\sqrt{15}+3\sqrt{2}}\end{aligned}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\begin{aligned}&\frac{7\sqrt{3}}{{3}^{\frac{1\times 1}{2\times 2}}}-\frac{{2}^{\sqrt{5}}}{\sqrt{6}\sqrt{55}}\\&\frac{3\sqrt{2}}{\sqrt{15}+3\sqrt{2}}\end{aligned}\]
Simplify \(1\times 1\) to \(1\).
\[\begin{aligned}&\frac{7\sqrt{3}}{\sqrt[2\times 2]{3}}-\frac{{2}^{\sqrt{5}}}{\sqrt{6}\sqrt{55}}\\&\frac{3\sqrt{2}}{\sqrt{15}+3\sqrt{2}}\end{aligned}\]
Simplify \(2\times 2\) to \(4\).
\[\begin{aligned}&\frac{7\sqrt{3}}{\sqrt[4]{3}}-\frac{{2}^{\sqrt{5}}}{\sqrt{6}\sqrt{55}}\\&\frac{3\sqrt{2}}{\sqrt{15}+3\sqrt{2}}\end{aligned}\]
Simplify \(\sqrt{6}\sqrt{55}\) to \(\sqrt{330}\).
\[\begin{aligned}&\frac{7\sqrt{3}}{\sqrt[4]{3}}-\frac{{2}^{\sqrt{5}}}{\sqrt{330}}\\&\frac{3\sqrt{2}}{\sqrt{15}+3\sqrt{2}}\end{aligned}\]
Use Quotient Rule: \(\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}\).
\[\begin{aligned}&7\sqrt[2}-\frac{1}{4]{3}-\frac{{2}^{\sqrt{5}}}{\sqrt{330}}\\&\frac{3\sqrt{2}}{\sqrt{15}+3\sqrt{2}}\end{aligned}\]
Simplify \(\frac{1}{2}-\frac{1}{4}\) to \(\frac{1}{4}\).
\[\begin{aligned}&7\sqrt[4]{3}-\frac{{2}^{\sqrt{5}}}{\sqrt{330}}\\&\frac{3\sqrt{2}}{\sqrt{15}+3\sqrt{2}}\end{aligned}\]
7*3^(1/4)-2^sqrt(5)/sqrt(330);(3*sqrt(2))/(sqrt(15)+3*sqrt(2))
