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\frac{\sqrt{432}}{\sqrt{7}}
Rewrite the square root of the division \sqrt{\frac{432}{7}} as the division of square roots \frac{\sqrt{432}}{\sqrt{7}}.
\frac{12\sqrt{3}}{\sqrt{7}}
Factor 432=12^{2}\times 3. Rewrite the square root of the product \sqrt{12^{2}\times 3} as the product of square roots \sqrt{12^{2}}\sqrt{3}. Take the square root of 12^{2}.
\frac{12\sqrt{3}\sqrt{7}}{\left(\sqrt{7}\right)^{2}}
Rationalize the denominator of \frac{12\sqrt{3}}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.
\frac{12\sqrt{3}\sqrt{7}}{7}
The square of \sqrt{7} is 7.
\frac{12\sqrt{21}}{7}
To multiply \sqrt{3} and \sqrt{7}, multiply the numbers under the square root.