Solve 4sqrt{2}-3sqrt{6}div2sqrt{2}

$$4 \sqrt{ 2 } -3 \sqrt{ 6 } \div 2 \sqrt{ 2 }$$

Evaluate

$$4\sqrt{2}-3\sqrt{3}\approx 0.460701827$$

Solution Steps

Express \frac{3\sqrt{6}}{2}\sqrt{2} as a single fraction.

$$4\sqrt{2}-\frac{3\sqrt{6}\sqrt{2}}{2}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

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

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

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

Multiply 3 and 2 to get 6.

$$4\sqrt{2}-\frac{6\sqrt{3}}{2}$$

Divide 6\sqrt{3} by 2 to get 3\sqrt{3}.

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

Factor

$$4 \sqrt{2} - 3 \sqrt{3} = 0.460701827$$