Solve sqrt{52}*4sqrt{2}divsqrt{13}

$$\sqrt { 52 } \times 4 \sqrt { 2 } \div \sqrt { 13 }$$

Evaluate

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

Solution Steps

Factor 52=2\times 26. Rewrite the square root of the product \sqrt{2\times 26} as the product of square roots \sqrt{2}\sqrt{26}.

$$\frac{4\sqrt{2}\sqrt{26}\sqrt{2}}{\sqrt{13}}$$

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

$$\frac{4\times 2\sqrt{26}}{\sqrt{13}}$$

Multiply 4 and 2 to get 8.

$$\frac{8\sqrt{26}}{\sqrt{13}}$$

Rationalize the denominator of \frac{8\sqrt{26}}{\sqrt{13}} by multiplying numerator and denominator by \sqrt{13}.

$$\frac{8\sqrt{26}\sqrt{13}}{\left(\sqrt{13}\right)^{2}}$$

The square of \sqrt{13} is 13.

$$\frac{8\sqrt{26}\sqrt{13}}{13}$$

Factor 26=13\times 2. Rewrite the square root of the product \sqrt{13\times 2} as the product of square roots \sqrt{13}\sqrt{2}.

$$\frac{8\sqrt{13}\sqrt{2}\sqrt{13}}{13}$$

Multiply \sqrt{13} and \sqrt{13} to get 13.

$$\frac{8\times 13\sqrt{2}}{13}$$

Cancel out 13 and 13.

$$8\sqrt{2}$$