Solve 1/22sqrt{605}+1/30sqrt{1125}-1/34sqrt{1445}

$$\frac { 1 } { 22 } \sqrt { 605 } + \frac { 1 } { 30 } \sqrt { 1125 } - \frac { 1 } { 34 } \sqrt { 1445 }$$

Evaluate

$$\frac{\sqrt{5}}{2}\approx 1.118033989$$

Solution Steps

Factor 605=11^{2}\times 5. Rewrite the square root of the product \sqrt{11^{2}\times 5} as the product of square roots \sqrt{11^{2}}\sqrt{5}. Take the square root of 11^{2}.

$$\frac{1}{22}\times 11\sqrt{5}+\frac{1}{30}\sqrt{1125}-\frac{1}{34}\sqrt{1445}$$

Multiply \frac{1}{22} and 11 to get \frac{11}{22}.

$$\frac{11}{22}\sqrt{5}+\frac{1}{30}\sqrt{1125}-\frac{1}{34}\sqrt{1445}$$

Reduce the fraction \frac{11}{22} to lowest terms by extracting and canceling out 11.

$$\frac{1}{2}\sqrt{5}+\frac{1}{30}\sqrt{1125}-\frac{1}{34}\sqrt{1445}$$

Factor 1125=15^{2}\times 5. Rewrite the square root of the product \sqrt{15^{2}\times 5} as the product of square roots \sqrt{15^{2}}\sqrt{5}. Take the square root of 15^{2}.

$$\frac{1}{2}\sqrt{5}+\frac{1}{30}\times 15\sqrt{5}-\frac{1}{34}\sqrt{1445}$$

Multiply \frac{1}{30} and 15 to get \frac{15}{30}.

$$\frac{1}{2}\sqrt{5}+\frac{15}{30}\sqrt{5}-\frac{1}{34}\sqrt{1445}$$

Reduce the fraction \frac{15}{30} to lowest terms by extracting and canceling out 15.

$$\frac{1}{2}\sqrt{5}+\frac{1}{2}\sqrt{5}-\frac{1}{34}\sqrt{1445}$$

Combine \frac{1}{2}\sqrt{5} and \frac{1}{2}\sqrt{5} to get \sqrt{5}.

$$\sqrt{5}-\frac{1}{34}\sqrt{1445}$$

Factor 1445=17^{2}\times 5. Rewrite the square root of the product \sqrt{17^{2}\times 5} as the product of square roots \sqrt{17^{2}}\sqrt{5}. Take the square root of 17^{2}.

$$\sqrt{5}-\frac{1}{34}\times 17\sqrt{5}$$

Express -\frac{1}{34}\times 17 as a single fraction.

$$\sqrt{5}+\frac{-17}{34}\sqrt{5}$$

Reduce the fraction \frac{-17}{34} to lowest terms by extracting and canceling out 17.

$$\sqrt{5}-\frac{1}{2}\sqrt{5}$$

Combine \sqrt{5} and -\frac{1}{2}\sqrt{5} to get \frac{1}{2}\sqrt{5}.

$$\frac{1}{2}\sqrt{5}$$