Solve (1/2sqrt{2}*1/2sqrt{3}.1+(1/2*1/2sqrt{2})

$$( \frac { 1 } { 2 } \sqrt { 2 } \times \frac { 1 } { 2 } \sqrt { 3 } .1 + ( \frac { 1 } { 2 } \times \frac { 1 } { 2 } \sqrt { 2 } )$$

Evaluate

$$\frac{\sqrt{2}\left(\sqrt{3}+10\right)}{40}\approx 0.414790634$$

Solution Steps

Convert decimal number 0.1 to fraction \frac{1}{10}.

$$\frac{1}{10}\times \frac{1}{2}\sqrt{2}\times \frac{1}{2}\sqrt{3}+\frac{1}{2}\times \frac{1}{2}\sqrt{2}$$

Multiply \frac{1}{10} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{10\times 2}\sqrt{2}\times \frac{1}{2}\sqrt{3}+\frac{1}{2}\times \frac{1}{2}\sqrt{2}$$

Do the multiplications in the fraction \frac{1\times 1}{10\times 2}.

$$\frac{1}{20}\sqrt{2}\times \frac{1}{2}\sqrt{3}+\frac{1}{2}\times \frac{1}{2}\sqrt{2}$$

Multiply \frac{1}{20} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 1}{20\times 2}\sqrt{2}\sqrt{3}+\frac{1}{2}\times \frac{1}{2}\sqrt{2}$$

Do the multiplications in the fraction \frac{1\times 1}{20\times 2}.

$$\frac{1}{40}\sqrt{2}\sqrt{3}+\frac{1}{2}\times \frac{1}{2}\sqrt{2}$$

To multiply \sqrt{2} and \sqrt{3}, multiply the numbers under the square root.

$$\frac{1}{40}\sqrt{6}+\frac{1}{2}\times \frac{1}{2}\sqrt{2}$$

Multiply \frac{1}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{40}\sqrt{6}+\frac{1\times 1}{2\times 2}\sqrt{2}$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 2}.

$$\frac{1}{40}\sqrt{6}+\frac{1}{4}\sqrt{2}$$

Factor

$$\frac{\sqrt{2} {(\sqrt{3} + 10)}}{40} = 0.4147906341628532$$