Solve sqrt{5^5*3^3}*sqrt{15}

$$\sqrt{ { 5 }^{ 5 } \times { 3 }^{ 3 } } \times \sqrt{ 15 }$$

Evaluate

$$1125$$

Solution Steps

Calculate 5 to the power of 5 and get 3125.

$$\sqrt{3125\times 3^{3}}\sqrt{15}$$

Calculate 3 to the power of 3 and get 27.

$$\sqrt{3125\times 27}\sqrt{15}$$

Multiply 3125 and 27 to get 84375.

$$\sqrt{84375}\sqrt{15}$$

Factor 84375=75^{2}\times 15. Rewrite the square root of the product \sqrt{75^{2}\times 15} as the product of square roots \sqrt{75^{2}}\sqrt{15}. Take the square root of 75^{2}.

$$75\sqrt{15}\sqrt{15}$$

Multiply \sqrt{15} and \sqrt{15} to get 15.

$$75\times 15$$

Multiply 75 and 15 to get 1125.

$$1125$$

Factor

$$3^{2}\times 5^{3}$$