Solve 14(2)sqrt{2^2+6^2}+3.14(2)^2

$$14 ( 2 ) \sqrt { 2 ^ { 2 } + 6 ^ { 2 } } + 3.14 ( 2 ) ^ { 2 }$$

Evaluate

$$56\sqrt{10}+12.56\approx 189.647548969$$

Solution Steps

Multiply 14 and 2 to get 28.

$$28\sqrt{2^{2}+6^{2}}+3.14\times 2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$28\sqrt{4+6^{2}}+3.14\times 2^{2}$$

Calculate 6 to the power of 2 and get 36.

$$28\sqrt{4+36}+3.14\times 2^{2}$$

Add 4 and 36 to get 40.

$$28\sqrt{40}+3.14\times 2^{2}$$

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}.

$$28\times 2\sqrt{10}+3.14\times 2^{2}$$

Multiply 28 and 2 to get 56.

$$56\sqrt{10}+3.14\times 2^{2}$$

Calculate 2 to the power of 2 and get 4.

$$56\sqrt{10}+3.14\times 4$$

Multiply 3.14 and 4 to get 12.56.

$$56\sqrt{10}+12.56$$

Factor

$$56 \sqrt{10} + 12.56 = 189.647548969$$