Solve frac{sqrt{75}-sqrt{108}+sqrt{147}}{sqrt{108}}

$$\frac { \sqrt { 75 } - \sqrt { 108 } + \sqrt { 147 } } { \sqrt { 108 } }$$

Evaluate

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Solution Steps

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$\frac{5\sqrt{3}-\sqrt{108}+\sqrt{147}}{\sqrt{108}}$$

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

$$\frac{5\sqrt{3}-6\sqrt{3}+\sqrt{147}}{\sqrt{108}}$$

Combine 5\sqrt{3} and -6\sqrt{3} to get -\sqrt{3}.

$$\frac{-\sqrt{3}+\sqrt{147}}{\sqrt{108}}$$

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}.

$$\frac{-\sqrt{3}+7\sqrt{3}}{\sqrt{108}}$$

Combine -\sqrt{3} and 7\sqrt{3} to get 6\sqrt{3}.

$$\frac{6\sqrt{3}}{\sqrt{108}}$$

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

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

Cancel out 6\sqrt{3} in both numerator and denominator.

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Factor

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