Solve 5^3sqrt{128}-3^3sqrt{250}

$${ 5 }^{ 3 } \sqrt{ 128 } - { 3 }^{ 3 } \sqrt{ 250 }$$

Evaluate

$$1000\sqrt{2}-135\sqrt{10}\approx 987.30607825$$

Solution Steps

Calculate 5 to the power of 3 and get 125.

$$125\sqrt{128}-3^{3}\sqrt{250}$$

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}.

$$125\times 8\sqrt{2}-3^{3}\sqrt{250}$$

Multiply 125 and 8 to get 1000.

$$1000\sqrt{2}-3^{3}\sqrt{250}$$

Calculate 3 to the power of 3 and get 27.

$$1000\sqrt{2}-27\sqrt{250}$$

Factor 250=5^{2}\times 10. Rewrite the square root of the product \sqrt{5^{2}\times 10} as the product of square roots \sqrt{5^{2}}\sqrt{10}. Take the square root of 5^{2}.

$$1000\sqrt{2}-27\times 5\sqrt{10}$$

Multiply 27 and 5 to get 135.

$$1000\sqrt{2}-135\sqrt{10}$$