Solve frac{sqrt{(-3)^2+(-6)^2}}{sqrt{9+36}}

$$\frac { \sqrt { ( - 3 ) ^ { 2 } + ( - 6 ) ^ { 2 } } } { \sqrt { 9 + 36 } }$$

Evaluate

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Solution Steps

Calculate -3 to the power of 2 and get 9.

$$\frac{\sqrt{9+\left(-6\right)^{2}}}{\sqrt{9+36}}$$

Calculate -6 to the power of 2 and get 36.

$$\frac{\sqrt{9+36}}{\sqrt{9+36}}$$

Add 9 and 36 to get 45.

$$\frac{\sqrt{45}}{\sqrt{9+36}}$$

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}.

$$\frac{3\sqrt{5}}{\sqrt{9+36}}$$

Add 9 and 36 to get 45.

$$\frac{3\sqrt{5}}{\sqrt{45}}$$

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}.

$$\frac{3\sqrt{5}}{3\sqrt{5}}$$

Cancel out 3\sqrt{5} in both numerator and denominator.

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Factor

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