Solve 3^3sqrt{10}*5^3sqrt{30}

$${ 3 }^{ 3 } \sqrt{ 10 } \times { 5 }^{ 3 } \sqrt{ 30 }$$

Evaluate

$$33750\sqrt{3}\approx 58456.71475545$$

Solution Steps

Factor 30=10\times 3. Rewrite the square root of the product \sqrt{10\times 3} as the product of square roots \sqrt{10}\sqrt{3}.

$$3^{3}\sqrt{10}\times 5^{3}\sqrt{10}\sqrt{3}$$

Multiply \sqrt{10} and \sqrt{10} to get 10.

$$3^{3}\times 10\times 5^{3}\sqrt{3}$$

Calculate 3 to the power of 3 and get 27.

$$27\times 10\times 5^{3}\sqrt{3}$$

Multiply 27 and 10 to get 270.

$$270\times 5^{3}\sqrt{3}$$

Calculate 5 to the power of 3 and get 125.

$$270\times 125\sqrt{3}$$

Multiply 270 and 125 to get 33750.

$$33750\sqrt{3}$$