Solve 2pi*sqrt{32}*(sqrt{32}+sqrt{128})

$$2 \pi \times \sqrt{ 32 } \times ( \sqrt{ 32 } + \sqrt{ 128 } )$$

Evaluate

$$192\pi \approx 603.185789489$$

Solution Steps

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$2\pi \times 4\sqrt{2}\left(\sqrt{32}+\sqrt{128}\right)$$

Multiply 2 and 4 to get 8.

$$8\pi \sqrt{2}\left(\sqrt{32}+\sqrt{128}\right)$$

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$8\pi \sqrt{2}\left(4\sqrt{2}+\sqrt{128}\right)$$

Factor 128=8^{2}\times 2. Rewrite the square root of the product \sqrt{8^{2}\times 2} as the product of square roots \sqrt{8^{2}}\sqrt{2}. Take the square root of 8^{2}.

$$8\pi \sqrt{2}\left(4\sqrt{2}+8\sqrt{2}\right)$$

Combine 4\sqrt{2} and 8\sqrt{2} to get 12\sqrt{2}.

$$8\pi \sqrt{2}\times 12\sqrt{2}$$

Multiply 8 and 12 to get 96.

$$96\pi \sqrt{2}\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$96\pi \times 2$$

Multiply 96 and 2 to get 192.

$$192\pi$$