Solve (3sqrt{2}+bsqrt{2})*(1/4sqrt{2})

$$( 3 \sqrt { 2 } + b \sqrt { 2 } ) \cdot ( \frac { 1 } { 4 } \sqrt { 2 } )$$

Evaluate

$$\frac{b+3}{2}$$

Solution Steps

Use the distributive property to multiply 3\sqrt{2}+b\sqrt{2} by \frac{1}{4}.

$$\left(3\sqrt{2}\times \frac{1}{4}+b\sqrt{2}\times \frac{1}{4}\right)\sqrt{2}$$

Multiply 3 and \frac{1}{4} to get \frac{3}{4}.

$$\left(\frac{3}{4}\sqrt{2}+b\sqrt{2}\times \frac{1}{4}\right)\sqrt{2}$$

Use the distributive property to multiply \frac{3}{4}\sqrt{2}+b\sqrt{2}\times \frac{1}{4} by \sqrt{2}.

$$\frac{3}{4}\sqrt{2}\sqrt{2}+b\sqrt{2}\times \frac{1}{4}\sqrt{2}$$

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

$$\frac{3}{4}\times 2+b\sqrt{2}\times \frac{1}{4}\sqrt{2}$$

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

$$\frac{3}{4}\times 2+b\times 2\times \frac{1}{4}$$

Express \frac{3}{4}\times 2 as a single fraction.

$$\frac{3\times 2}{4}+b\times 2\times \frac{1}{4}$$

Multiply 3 and 2 to get 6.

$$\frac{6}{4}+b\times 2\times \frac{1}{4}$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}+b\times 2\times \frac{1}{4}$$

Multiply 2 and \frac{1}{4} to get \frac{2}{4}.

$$\frac{3}{2}+b\times \frac{2}{4}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{3}{2}+b\times \frac{1}{2}$$

Factor

$$\frac{b+3}{2}$$