Solve 4sqrt{192}divsqrt{24}

$$4 \sqrt { 192 } \div \sqrt { 24 }$$

Evaluate

$$8\sqrt{2}\approx 11.313708499$$

Solution Steps

Factor 192=8^{2}\times 3. Rewrite the square root of the product \sqrt{8^{2}\times 3} as the product of square roots \sqrt{8^{2}}\sqrt{3}. Take the square root of 8^{2}.

$$\frac{4\times 8\sqrt{3}}{\sqrt{24}}$$

Multiply 4 and 8 to get 32.

$$\frac{32\sqrt{3}}{\sqrt{24}}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$\frac{32\sqrt{3}}{2\sqrt{6}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{16\sqrt{3}}{\sqrt{6}}$$

Rationalize the denominator of \frac{16\sqrt{3}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{16\sqrt{3}\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{16\sqrt{3}\sqrt{6}}{6}$$

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

$$\frac{16\sqrt{3}\sqrt{3}\sqrt{2}}{6}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{16\times 3\sqrt{2}}{6}$$

Multiply 16 and 3 to get 48.

$$\frac{48\sqrt{2}}{6}$$

Divide 48\sqrt{2} by 6 to get 8\sqrt{2}.

$$8\sqrt{2}$$