Solve frac{10sqrt{6}}{sqrt{48}}divfrac{5sqrt{2}}{sqrt{49}}

$$\frac { 10 \sqrt { 6 } } { \sqrt { 48 } } \div \frac { 5 \sqrt { 2 } } { \sqrt { 49 } }$$

Evaluate

$$\frac{7}{2}=3.5$$

Solution Steps

Divide \frac{10\sqrt{6}}{\sqrt{48}} by \frac{5\sqrt{2}}{\sqrt{49}} by multiplying \frac{10\sqrt{6}}{\sqrt{48}} by the reciprocal of \frac{5\sqrt{2}}{\sqrt{49}}.

$$\frac{10\sqrt{6}\sqrt{49}}{\sqrt{48}\times 5\sqrt{2}}$$

Cancel out 5 in both numerator and denominator.

$$\frac{2\sqrt{6}\sqrt{49}}{\sqrt{2}\sqrt{48}}$$

Calculate the square root of 49 and get 7.

$$\frac{2\sqrt{6}\times 7}{\sqrt{2}\sqrt{48}}$$

Multiply 2 and 7 to get 14.

$$\frac{14\sqrt{6}}{\sqrt{2}\sqrt{48}}$$

Factor 48=2\times 24. Rewrite the square root of the product \sqrt{2\times 24} as the product of square roots \sqrt{2}\sqrt{24}.

$$\frac{14\sqrt{6}}{\sqrt{2}\sqrt{2}\sqrt{24}}$$

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

$$\frac{14\sqrt{6}}{2\sqrt{24}}$$

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}.

$$\frac{14\sqrt{6}}{2\times 2\sqrt{6}}$$

Multiply 2 and 2 to get 4.

$$\frac{14\sqrt{6}}{4\sqrt{6}}$$

Cancel out 2\sqrt{6} in both numerator and denominator.

$$\frac{7}{2}$$

Factor

$$\frac{7}{2} = 3\frac{1}{2} = 3.5$$