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

glamrockqueen7 2021-08-04 Answered
To calculate: \(\displaystyle{a}\div\sqrt{{{b}}}\)
The simplified value of the radical expression.

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Expert Answer

wheezym
Answered 2021-08-05 Author has 24070 answers

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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content_user
Answered 2021-10-29 Author has 11827 answers

Answer is given below (on video)

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