Solve 3sqrt{8}div4sqrt{12}

$$3 \sqrt{ 8 } \div 4 \sqrt{ 12 }$$

Evaluate

$$3\sqrt{6}\approx 7.348469228$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{3\times 2\sqrt{2}}{4}\sqrt{12}$$

Multiply 3 and 2 to get 6.

$$\frac{6\sqrt{2}}{4}\sqrt{12}$$

Divide 6\sqrt{2} by 4 to get \frac{3}{2}\sqrt{2}.

$$\frac{3}{2}\sqrt{2}\sqrt{12}$$

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}.

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

Cancel out 2 and 2.

$$3\sqrt{2}\sqrt{3}$$

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

$$3\sqrt{6}$$