Solve 4+5^2*4^2sqrt{52}

$$4+ { 5 }^{ 2 } \times { 4 }^{ 2 } \sqrt{ 52 }$$

Evaluate

$$800\sqrt{13}+4\approx 2888.441020371$$

Solution Steps

Calculate 5 to the power of 2 and get 25.

$$4+25\times 4^{2}\sqrt{52}$$

Calculate 4 to the power of 2 and get 16.

$$4+25\times 16\sqrt{52}$$

Multiply 25 and 16 to get 400.

$$4+400\sqrt{52}$$

Factor 52=2^{2}\times 13. Rewrite the square root of the product \sqrt{2^{2}\times 13} as the product of square roots \sqrt{2^{2}}\sqrt{13}. Take the square root of 2^{2}.

$$4+400\times 2\sqrt{13}$$

Multiply 400 and 2 to get 800.

$$4+800\sqrt{13}$$

Factor

$$4 {(200 \sqrt{13} + 1)} = 2888.441020371$$