Solve frac{sqrt{126}*sqrt{63}*sqrt{4}}{sqrt{147}*sqrt{243}}

$$\frac { \sqrt { 126 } \times \sqrt { 63 } \times \sqrt { 4 } } { \sqrt { 147 } \times \sqrt { 243 } }$$

Evaluate

$$\frac{2\sqrt{2}}{3}\approx 0.942809042$$

Solution Steps

Factor 126=63\times 2. Rewrite the square root of the product \sqrt{63\times 2} as the product of square roots \sqrt{63}\sqrt{2}.

$$\frac{\sqrt{63}\sqrt{2}\sqrt{63}\sqrt{4}}{\sqrt{147}\sqrt{243}}$$

Multiply \sqrt{63} and \sqrt{63} to get 63.

$$\frac{63\sqrt{2}\sqrt{4}}{\sqrt{147}\sqrt{243}}$$

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

$$\frac{63\sqrt{2}\sqrt{2}\sqrt{2}}{\sqrt{147}\sqrt{243}}$$

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

$$\frac{63\times 2\sqrt{2}}{\sqrt{147}\sqrt{243}}$$

Multiply 63 and 2 to get 126.

$$\frac{126\sqrt{2}}{\sqrt{147}\sqrt{243}}$$

Factor 147=7^{2}\times 3. Rewrite the square root of the product \sqrt{7^{2}\times 3} as the product of square roots \sqrt{7^{2}}\sqrt{3}. Take the square root of 7^{2}.

$$\frac{126\sqrt{2}}{7\sqrt{3}\sqrt{243}}$$

Factor 243=9^{2}\times 3. Rewrite the square root of the product \sqrt{9^{2}\times 3} as the product of square roots \sqrt{9^{2}}\sqrt{3}. Take the square root of 9^{2}.

$$\frac{126\sqrt{2}}{7\sqrt{3}\times 9\sqrt{3}}$$

Multiply 7 and 9 to get 63.

$$\frac{126\sqrt{2}}{63\sqrt{3}\sqrt{3}}$$

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

$$\frac{126\sqrt{2}}{63\times 3}$$

Multiply 63 and 3 to get 189.

$$\frac{126\sqrt{2}}{189}$$

Divide 126\sqrt{2} by 189 to get \frac{2}{3}\sqrt{2}.

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