Solve 48sqrt{3}+24sqrt{3}+sqrt{48sqrt{3}24sqrt{3}}

$$48 \sqrt{ 3 } +24 \sqrt{ 3 } + \sqrt{ 48 \sqrt{ 3 } 24 \sqrt{ 3 } }$$

Evaluate

$$24\left(\sqrt{6}+3\sqrt{3}\right)\approx 183.495411972$$

Solution Steps

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$48\sqrt{3}+24\sqrt{3}+\sqrt{24\times 48\times 3}$$

Combine 48\sqrt{3} and 24\sqrt{3} to get 72\sqrt{3}.

$$72\sqrt{3}+\sqrt{24\times 48\times 3}$$

Multiply 24 and 48 to get 1152.

$$72\sqrt{3}+\sqrt{1152\times 3}$$

Multiply 1152 and 3 to get 3456.

$$72\sqrt{3}+\sqrt{3456}$$

Factor 3456=24^{2}\times 6. Rewrite the square root of the product \sqrt{24^{2}\times 6} as the product of square roots \sqrt{24^{2}}\sqrt{6}. Take the square root of 24^{2}.

$$72\sqrt{3}+24\sqrt{6}$$