# The simplified form of the expressiondisplaystyle{sqrt[{{3}}]{{a}}}{sqrt[{{6}}]{{a}}} text{in radicalnotation is} sqrt{a}.

The simplified form of the expression
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Fatema Sutton
Formula used:
Step 1: First convert the radical expression into exponential expressions.
Step 2: Simplify the exponential expression by adding exponents or subtracting exponents.
Step 3: Now, convert the exponential expression into radical expression.
Positive rational exponents:
$\sqrt[m]{{a}^{n}}={a}^{n\text{/}m}\phantom{\rule{1em}{0ex}}\text{or}\phantom{\rule{1em}{0ex}}{a}^{n\text{/}m}=\sqrt[m]{{a}^{n}}$
Power of product:
${\left({x}^{m}\right)}^{n}={x}^{m\cdot n}$
Calculation:
Consider the provided expression, $\sqrt[3]{a}\sqrt[6]{a}$
Now, convert the provided radical expression into the exponential notationusing formula of positive rational exponents $\sqrt[m]{{a}^{n}}={a}^{n\text{/}m}$
$\sqrt[3]{a}\sqrt[6]{a}={a}^{1\text{/}3}\cdot {a}^{1\text{/}6}$ ...... (1)
Now, solve the exponents.
$\frac{1}{3}+\frac{1}{6}=\frac{2+1}{6}$
$=\frac{3}{6}$ ...... (2)
$=\frac{1}{2}$
Now put equation (2) in equation (1),
${a}^{1\text{/}3}\cdot {a}^{1\text{/}6}={a}^{1\text{/}2}$
Now convert the exponential expression into radical expression using formula
${a}^{n\text{/}m}=\sqrt[m]{{a}^{n}}.$
${a}^{1\text{/}2}=\sqrt{a}$
Therefore, the simplified form of the expression
Jeffrey Jordon