Solve sqrt{2^4}*sqrt{3^2}*sqrt{5}+sqrt{2^2}*sqrt{5^2}*sqrt{5}

$$\sqrt{ { 2 }^{ 4 } } \times \sqrt{ { 3 }^{ 2 } } \times \sqrt{ 5 } + \sqrt{ { 2 }^{ 2 } } \times \sqrt{ { 5 }^{ 2 } } \times \sqrt{ 5 }$$

Evaluate

$$22\sqrt{5}\approx 49.193495505$$

Solution Steps

Calculate 2 to the power of 4 and get 16.

$$\sqrt{16}\sqrt{3^{2}}\sqrt{5}+\sqrt{2^{2}}\sqrt{5^{2}}\sqrt{5}$$

Calculate the square root of 16 and get 4.

$$4\sqrt{3^{2}}\sqrt{5}+\sqrt{2^{2}}\sqrt{5^{2}}\sqrt{5}$$

Calculate 3 to the power of 2 and get 9.

$$4\sqrt{9}\sqrt{5}+\sqrt{2^{2}}\sqrt{5^{2}}\sqrt{5}$$

Calculate the square root of 9 and get 3.

$$4\times 3\sqrt{5}+\sqrt{2^{2}}\sqrt{5^{2}}\sqrt{5}$$

Multiply 4 and 3 to get 12.

$$12\sqrt{5}+\sqrt{2^{2}}\sqrt{5^{2}}\sqrt{5}$$

Calculate 2 to the power of 2 and get 4.

$$12\sqrt{5}+\sqrt{4}\sqrt{5^{2}}\sqrt{5}$$

Calculate the square root of 4 and get 2.

$$12\sqrt{5}+2\sqrt{5^{2}}\sqrt{5}$$

Calculate 5 to the power of 2 and get 25.

$$12\sqrt{5}+2\sqrt{25}\sqrt{5}$$

Calculate the square root of 25 and get 5.

$$12\sqrt{5}+2\times 5\sqrt{5}$$

Multiply 2 and 5 to get 10.

$$12\sqrt{5}+10\sqrt{5}$$

Combine 12\sqrt{5} and 10\sqrt{5} to get 22\sqrt{5}.

$$22\sqrt{5}$$