Solve sin(1)sqrt{2}(sqrt{8}+sqrt{18})

$$\sin ( 1 ) \sqrt { 2 } ( \sqrt { 8 } + \sqrt { 18 } )$$

Evaluate

$$0.1745240643728351$$

Solution Steps

Evaluate trigonometric functions in the problem

$$0.01745240643728351 \sqrt{2} {(\sqrt{8} + \sqrt{18})}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$0.01745240643728351\sqrt{2}\left(2\sqrt{2}+\sqrt{18}\right)$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$0.01745240643728351\sqrt{2}\left(2\sqrt{2}+3\sqrt{2}\right)$$

Combine 2\sqrt{2} and 3\sqrt{2} to get 5\sqrt{2}.

$$0.01745240643728351\sqrt{2}\times 5\sqrt{2}$$

Multiply 0.01745240643728351 and 5 to get 0.08726203218641755.

$$0.08726203218641755\sqrt{2}\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$0.08726203218641755\times 2$$

Multiply 0.08726203218641755 and 2 to get 0.1745240643728351.

$$0.1745240643728351$$

Factor

$$\frac{7 \cdot 11 \cdot 154849 \cdot 146371387}{2 ^ {16} \cdot 5 ^ {16}} = 0.1745240643728351$$