Solve 96sqrt{4^2+left(4^2right)^2}

$$96 \sqrt{ { 4 }^{ 2 } + { \left( { 4 }^{ 2 } \right) }^{ 2 } }$$

Evaluate

$$384\sqrt{17}\approx 1583.272560237$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$96\sqrt{4^{2}+4^{4}}$$

Calculate 4 to the power of 2 and get 16.

$$96\sqrt{16+4^{4}}$$

Calculate 4 to the power of 4 and get 256.

$$96\sqrt{16+256}$$

Add 16 and 256 to get 272.

$$96\sqrt{272}$$

Factor 272=4^{2}\times 17. Rewrite the square root of the product \sqrt{4^{2}\times 17} as the product of square roots \sqrt{4^{2}}\sqrt{17}. Take the square root of 4^{2}.

$$96\times 4\sqrt{17}$$

Multiply 96 and 4 to get 384.

$$384\sqrt{17}$$