Solve sqrt{1024^2{left(sqrt{3}right)}^2+1024^2}

$$\sqrt{ { 1024 }^{ 2 } { \left( \sqrt{ 3 } \right) }^{ 2 } + { 1024 }^{ 2 } }$$

Evaluate

$$2048$$

Solution Steps

Calculate 1024 to the power of 2 and get 1048576.

$$\sqrt{1048576\left(\sqrt{3}\right)^{2}+1024^{2}}$$

The square of \sqrt{3} is 3.

$$\sqrt{1048576\times 3+1024^{2}}$$

Multiply 1048576 and 3 to get 3145728.

$$\sqrt{3145728+1024^{2}}$$

Calculate 1024 to the power of 2 and get 1048576.

$$\sqrt{3145728+1048576}$$

Add 3145728 and 1048576 to get 4194304.

$$\sqrt{4194304}$$

Calculate the square root of 4194304 and get 2048.

$$2048$$

Factor

$$2^{11}$$