Solve 3(sqrt{2}+sqrt{3})+2(sqrt{2}-2sqrt{3})

$$3 ( \sqrt { 2 } + \sqrt { 3 } ) + 2 ( \sqrt { 2 } - 2 \sqrt { 3 } )$$

Evaluate

$$5\sqrt{2}-\sqrt{3}\approx 5.339017004$$

Solution Steps

Use the distributive property to multiply 3 by \sqrt{2}+\sqrt{3}.

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

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

$$3\sqrt{2}+3\sqrt{3}+2\sqrt{2}-4\sqrt{3}$$

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

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

Combine 3\sqrt{3} and -4\sqrt{3} to get -\sqrt{3}.

$$5\sqrt{2}-\sqrt{3}$$