Solve frac{sqrt{20}-6sqrt{5}}{2sqrt{45}-2sqrt{5}}

$$\frac { \sqrt { 20 } - 6 \sqrt { 5 } } { 2 \sqrt { 45 } - 2 \sqrt { 5 } }$$

Evaluate

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Solution Steps

Factor 20=2^{2}\times 5. Rewrite the square root of the product \sqrt{2^{2}\times 5} as the product of square roots \sqrt{2^{2}}\sqrt{5}. Take the square root of 2^{2}.

$$\frac{2\sqrt{5}-6\sqrt{5}}{2\sqrt{45}-2\sqrt{5}}$$

Combine 2\sqrt{5} and -6\sqrt{5} to get -4\sqrt{5}.

$$\frac{-4\sqrt{5}}{2\sqrt{45}-2\sqrt{5}}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$\frac{-4\sqrt{5}}{2\times 3\sqrt{5}-2\sqrt{5}}$$

Multiply 2 and 3 to get 6.

$$\frac{-4\sqrt{5}}{6\sqrt{5}-2\sqrt{5}}$$

Combine 6\sqrt{5} and -2\sqrt{5} to get 4\sqrt{5}.

$$\frac{-4\sqrt{5}}{4\sqrt{5}}$$

Cancel out 4\sqrt{5} in both numerator and denominator.

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Factor

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