Solve frac{sqrt{147}+sqrt{48}}{sqrt{363}}

$$\frac { \sqrt { 147 } + \sqrt { 48 } } { \sqrt { 363 } }$$

Evaluate

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Solution Steps

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}.

$$\frac{7\sqrt{3}+\sqrt{48}}{\sqrt{363}}$$

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}.

$$\frac{7\sqrt{3}+4\sqrt{3}}{\sqrt{363}}$$

Combine 7\sqrt{3} and 4\sqrt{3} to get 11\sqrt{3}.

$$\frac{11\sqrt{3}}{\sqrt{363}}$$

Factor 363=11^{2}\times 3. Rewrite the square root of the product \sqrt{11^{2}\times 3} as the product of square roots \sqrt{11^{2}}\sqrt{3}. Take the square root of 11^{2}.

$$\frac{11\sqrt{3}}{11\sqrt{3}}$$

Cancel out 11\sqrt{3} in both numerator and denominator.

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Factor

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