# To calculate: a\div\sqrt{b} the simplified value of the radical expression.

To calculate: $$\displaystyle{a}\div\sqrt{{{b}}}$$
The simplified value of the radical expression.

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Step 1
Use this formula to solve:
$$\sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}$$ The product rule for radicals,
$$\sqrt[n]{a}=a^{1/n}$$ The relation between radical and rational exponent notation is expressed as.
Step 2
Use the prodict rule for radicals to simplify the expression,
$$\displaystyle{a}\div\sqrt{{{b}}}={\frac{{{a}}}{{\sqrt{{{b}}}}}}$$
$$\displaystyle={\frac{{{a}}}{{\sqrt{{{b}}}}}}\times{\frac{{\sqrt{{{b}}}}}{{\sqrt{{{b}}}}}}$$
$$\displaystyle={\frac{{{a}\sqrt{{{b}}}}}{{{\left(\sqrt{{{b}}}\right)}^{{{2}}}}}}$$
Use the relation between radical and rational exponent notation to simplify the expression,
$$\displaystyle{a}\div\sqrt{{{b}}}={\frac{{{a}\sqrt{{{b}}}}}{{{\left({b}^{{\frac{{1}}{{2}}}}\right)}^{{{2}}}}}}$$
$$\displaystyle={\frac{{{2}\sqrt{{{b}}}}}{{{\left({b}\right)}^{{{2}{\left(\frac{{1}}{{2}}\right)}}}}}}$$
$$\displaystyle={\frac{{{a}\sqrt{{{b}}}}}{{{b}}}}$$
Hence, the simplified value of the provided expression is $$\displaystyle{\frac{{{a}\sqrt{{{b}}}}}{{{b}}}}$$

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