Solve =3.14(2)sqrt{2^2+6^2}+3.14(2)^2

$$= 3.14 ( 2 ) \sqrt { 2 ^ { 2 } + 6 ^ { 2 } } + 3.14 ( 2 ) ^ { 2 }$$

Evaluate

$$\frac{314\left(\sqrt{10}+1\right)}{25}\approx 52.278207412$$

Solution Steps

Multiply 3.14 and 2 to get 6.28.

$$6.28\sqrt{2^{2}+6^{2}}+3.14\times 2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$6.28\sqrt{4+6^{2}}+3.14\times 2^{2}$$

Calculate 6 to the power of 2 and get 36.

$$6.28\sqrt{4+36}+3.14\times 2^{2}$$

Add 4 and 36 to get 40.

$$6.28\sqrt{40}+3.14\times 2^{2}$$

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$6.28\times 2\sqrt{10}+3.14\times 2^{2}$$

Multiply 6.28 and 2 to get 12.56.

$$12.56\sqrt{10}+3.14\times 2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$12.56\sqrt{10}+3.14\times 4$$

Multiply 3.14 and 4 to get 12.56.

$$12.56\sqrt{10}+12.56$$

Factor

$$\frac{314 {(\sqrt{10} + 1)}}{25} = 52.27820741171486$$