Solve 3sqrt{64}*sqrt{25}div3sqrt{8}

$$3 \sqrt{ 64 } \times \sqrt{ 25 } \div 3 \sqrt{ 8 }$$

Evaluate

$$80\sqrt{2}\approx 113.13708499$$

Solution Steps

Cancel out 3 and 3.

$$\sqrt{64}\sqrt{25}\sqrt{8}$$

To multiply \sqrt{64} and \sqrt{25}, multiply the numbers under the square root.

$$\sqrt{1600}\sqrt{8}$$

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

$$\sqrt{1600}\times 2\sqrt{2}$$

Factor 1600=2\times 800. Rewrite the square root of the product \sqrt{2\times 800} as the product of square roots \sqrt{2}\sqrt{800}.

$$\sqrt{2}\sqrt{800}\times 2\sqrt{2}$$

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

$$2\times 2\sqrt{800}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{800}$$

Factor 800=20^{2}\times 2. Rewrite the square root of the product \sqrt{20^{2}\times 2} as the product of square roots \sqrt{20^{2}}\sqrt{2}. Take the square root of 20^{2}.

$$4\times 20\sqrt{2}$$

Multiply 4 and 20 to get 80.

$$80\sqrt{2}$$