Solve (5)quad(sqrt{48}+1/4sqrt{6}+sqrt{27}

$$( 5 ) \quad ( \sqrt { 48 } + \frac { 1 } { 4 } \sqrt { 6 } + \sqrt { 27 }$$

Evaluate

$$\frac{5\left(\sqrt{6}+28\sqrt{3}\right)}{4}\approx 63.683640443$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$5\left(4\sqrt{3}+\frac{1}{4}\sqrt{6}+\sqrt{27}\right)$$

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}.

$$5\left(4\sqrt{3}+\frac{1}{4}\sqrt{6}+3\sqrt{3}\right)$$

Combine 4\sqrt{3} and 3\sqrt{3} to get 7\sqrt{3}.

$$5\left(7\sqrt{3}+\frac{1}{4}\sqrt{6}\right)$$

Use the distributive property to multiply 5 by 7\sqrt{3}+\frac{1}{4}\sqrt{6}.

$$35\sqrt{3}+5\times \frac{1}{4}\sqrt{6}$$

Multiply 5 and \frac{1}{4} to get \frac{5}{4}.

$$35\sqrt{3}+\frac{5}{4}\sqrt{6}$$

Factor

$$\frac{5 {(\sqrt{6} + 28 \sqrt{3})}}{4} = 63.68364044338968$$