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\sqrt{\frac{24+3}{4}}
Multiply 6 and 4 to get 24.
\sqrt{\frac{27}{4}}
Add 24 and 3 to get 27.
\frac{\sqrt{27}}{\sqrt{4}}
Rewrite the square root of the division \sqrt{\frac{27}{4}} as the division of square roots \frac{\sqrt{27}}{\sqrt{4}}.
\frac{3\sqrt{3}}{\sqrt{4}}
Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.
\frac{3\sqrt{3}}{2}
Calculate the square root of 4 and get 2.