Solve frac{sqrt{720}*sqrt{15}}{sqrt{600}}

$$\frac { \sqrt { 720 } \cdot \sqrt { 15 } } { \sqrt { 600 } }$$

Evaluate

$$3\sqrt{2}\approx 4.242640687$$

Solution Steps

Factor 720=15\times 48. Rewrite the square root of the product \sqrt{15\times 48} as the product of square roots \sqrt{15}\sqrt{48}.

$$\frac{\sqrt{15}\sqrt{48}\sqrt{15}}{\sqrt{600}}$$

Multiply \sqrt{15} and \sqrt{15} to get 15.

$$\frac{15\sqrt{48}}{\sqrt{600}}$$

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\frac{15\times 4\sqrt{3}}{\sqrt{600}}$$

Multiply 15 and 4 to get 60.

$$\frac{60\sqrt{3}}{\sqrt{600}}$$

Factor 600=10^{2}\times 6. Rewrite the square root of the product \sqrt{10^{2}\times 6} as the product of square roots \sqrt{10^{2}}\sqrt{6}. Take the square root of 10^{2}.

$$\frac{60\sqrt{3}}{10\sqrt{6}}$$

Cancel out 10 in both numerator and denominator.

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

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

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

The square of \sqrt{6} is 6.

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

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}.

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

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

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

Cancel out 6 and 6.

$$3\sqrt{2}$$