Solve {l}{3sqrt{24}+sqrt{50}}{*sqrt{48}}

$$\left. \begin{array} { l } { 3 \sqrt { 24 } + \sqrt { 50 } } \\ { \times \sqrt { 48 } } \end{array} \right.$$

Evaluate

$$26\sqrt{6}\approx 63.686733312$$

Solution Steps

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$3\times 2\sqrt{6}+\sqrt{50}\sqrt{48}$$

Multiply 3 and 2 to get 6.

$$6\sqrt{6}+\sqrt{50}\sqrt{48}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$6\sqrt{6}+5\sqrt{2}\sqrt{48}$$

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}.

$$6\sqrt{6}+5\sqrt{2}\times 4\sqrt{3}$$

Multiply 5 and 4 to get 20.

$$6\sqrt{6}+20\sqrt{2}\sqrt{3}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$6\sqrt{6}+20\sqrt{6}$$

Combine 6\sqrt{6} and 20\sqrt{6} to get 26\sqrt{6}.

$$26\sqrt{6}$$