Question

$$\sqrt{\frac{\alpha}{\beta}},\sqrt{\frac{\beta}{\alpha}}$$

Answer

$$(sqrt(e)*a^(3/2)*sqrt(l)*sqrt(p)*sqrt(h)*sqrt(t))/sqrt(b),sqrt(b)*sqrt(e)*sqrt(t)*sqrt(l)*sqrt(p)*sqrt(h)*sqrt(a)$$

Solution


Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\sqrt{\frac{alphaeta}{b}},\sqrt{bet\times \frac{a}{a}lpha}\]
Regroup terms.
\[\sqrt{\frac{aaalphte}{b}},\sqrt{bet\times \frac{a}{a}lpha}\]
Simplify  \(aaalphte\)  to  \({a}^{3}lphte\).
\[\sqrt{\frac{{a}^{3}lphte}{b}},\sqrt{bet\times \frac{a}{a}lpha}\]
Regroup terms.
\[\sqrt{\frac{e{a}^{3}lpht}{b}},\sqrt{bet\times \frac{a}{a}lpha}\]
Simplify  \(\sqrt{\frac{e{a}^{3}lpht}{b}}\)  to  \(\frac{\sqrt{e{a}^{3}lpht}}{\sqrt{b}}\).
\[\frac{\sqrt{e{a}^{3}lpht}}{\sqrt{b}},\sqrt{bet\times \frac{a}{a}lpha}\]
Use this rule: \(\sqrt{ab}=\sqrt{a}\sqrt{b}\).
\[\frac{\sqrt{{a}^{3}}\sqrt{elpht}}{\sqrt{b}},\sqrt{bet\times \frac{a}{a}lpha}\]
Simplify  \(\sqrt{{a}^{3}}\)  to  \({({a}^{3})}^{\frac{1}{2}}\).
\[\frac{{({a}^{3})}^{\frac{1}{2}}\sqrt{elpht}}{\sqrt{b}},\sqrt{bet\times \frac{a}{a}lpha}\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{{({a}^{3})}^{\frac{1}{2}}\sqrt{e}\sqrt{l}\sqrt{p}\sqrt{h}\sqrt{t}}{\sqrt{b}},\sqrt{bet\times \frac{a}{a}lpha}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{{a}^{\frac{3}{2}}\sqrt{e}\sqrt{l}\sqrt{p}\sqrt{h}\sqrt{t}}{\sqrt{b}},\sqrt{bet\times \frac{a}{a}lpha}\]
Regroup terms.
\[\frac{\sqrt{e}{a}^{\frac{3}{2}}\sqrt{l}\sqrt{p}\sqrt{h}\sqrt{t}}{\sqrt{b}},\sqrt{bet\times \frac{a}{a}lpha}\]
Cancel \(a\).
\[\frac{\sqrt{e}{a}^{\frac{3}{2}}\sqrt{l}\sqrt{p}\sqrt{h}\sqrt{t}}{\sqrt{b}},\sqrt{betlpha}\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{\sqrt{e}{a}^{\frac{3}{2}}\sqrt{l}\sqrt{p}\sqrt{h}\sqrt{t}}{\sqrt{b}},\sqrt{b}\sqrt{e}\sqrt{t}\sqrt{l}\sqrt{p}\sqrt{h}\sqrt{a}\]