Solve 3+5(3/4-sqrt{2})

$$3 + 5 ( \frac { 3 } { 4 } - \sqrt { 2 } )$$

Evaluate

$$\frac{27}{4}-5\sqrt{2}\approx -0.321067812$$

Solution Steps

Use the distributive property to multiply 5 by \frac{3}{4}-\sqrt{2}.

$$3+5\times \frac{3}{4}-5\sqrt{2}$$

Express 5\times \frac{3}{4} as a single fraction.

$$3+\frac{5\times 3}{4}-5\sqrt{2}$$

Multiply 5 and 3 to get 15.

$$3+\frac{15}{4}-5\sqrt{2}$$

Convert 3 to fraction \frac{12}{4}.

$$\frac{12}{4}+\frac{15}{4}-5\sqrt{2}$$

Since \frac{12}{4} and \frac{15}{4} have the same denominator, add them by adding their numerators.

$$\frac{12+15}{4}-5\sqrt{2}$$

Add 12 and 15 to get 27.

$$\frac{27}{4}-5\sqrt{2}$$

Factor

$$\frac{27 - 20 \sqrt{2}}{4} = -0.3210678118654755$$