Solve 3(sqrt{3}+sqrt{2})-4(sqrt{2}-sqrt{27})

$$3 ( \sqrt { 3 } + \sqrt { 2 } ) - 4 ( \sqrt { 2 } - \sqrt { 27 } )$$

Evaluate

$$15\sqrt{3}-\sqrt{2}\approx 24.566548551$$

Solution Steps

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

$$3\sqrt{3}+3\sqrt{2}-4\left(\sqrt{2}-\sqrt{27}\right)$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$3\sqrt{3}+3\sqrt{2}-4\left(\sqrt{2}-3\sqrt{3}\right)$$

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

$$3\sqrt{3}+3\sqrt{2}-4\sqrt{2}+12\sqrt{3}$$

Combine 3\sqrt{2} and -4\sqrt{2} to get -\sqrt{2}.

$$3\sqrt{3}-\sqrt{2}+12\sqrt{3}$$

Combine 3\sqrt{3} and 12\sqrt{3} to get 15\sqrt{3}.

$$15\sqrt{3}-\sqrt{2}$$