Solve 12sqrt{12}div2sqrt{2}+24sqrt{3}div2sqrt{2}-20sqrt{2}div2sqrt{2}

$$12 \sqrt{ 12 } \div 2 \sqrt{ 2 } +24 \sqrt{ 3 } \div 2 \sqrt{ 2 } -20 \sqrt{ 2 } \div 2 \sqrt{ 2 }$$

Evaluate

$$4\left(6\sqrt{6}-5\right)\approx 38.787753827$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$\frac{12\times 2\sqrt{3}}{2}\sqrt{2}+\frac{24\sqrt{3}}{2}\sqrt{2}-\frac{20\sqrt{2}}{2}\sqrt{2}$$

Multiply 12 and 2 to get 24.

$$\frac{24\sqrt{3}}{2}\sqrt{2}+\frac{24\sqrt{3}}{2}\sqrt{2}-\frac{20\sqrt{2}}{2}\sqrt{2}$$

Divide 24\sqrt{3} by 2 to get 12\sqrt{3}.

$$12\sqrt{3}\sqrt{2}+\frac{24\sqrt{3}}{2}\sqrt{2}-\frac{20\sqrt{2}}{2}\sqrt{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$12\sqrt{6}+\frac{24\sqrt{3}}{2}\sqrt{2}-\frac{20\sqrt{2}}{2}\sqrt{2}$$

Divide 24\sqrt{3} by 2 to get 12\sqrt{3}.

$$12\sqrt{6}+12\sqrt{3}\sqrt{2}-\frac{20\sqrt{2}}{2}\sqrt{2}$$

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$12\sqrt{6}+12\sqrt{6}-\frac{20\sqrt{2}}{2}\sqrt{2}$$

Combine 12\sqrt{6} and 12\sqrt{6} to get 24\sqrt{6}.

$$24\sqrt{6}-\frac{20\sqrt{2}}{2}\sqrt{2}$$

Divide 20\sqrt{2} by 2 to get 10\sqrt{2}.

$$24\sqrt{6}-10\sqrt{2}\sqrt{2}$$

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

$$24\sqrt{6}-10\times 2$$

Multiply 10 and 2 to get 20.

$$24\sqrt{6}-20$$

Factor

$$4 {(6 \sqrt{6} - 5)} = 38.787753827$$