Solve sqrt{5}+2sqrt{45}-3sqrt{125}=-8sqrt{5}

$$\sqrt { 5 } + 2 \sqrt { 45 } - 3 \sqrt { 125 } = - 8 \sqrt { 5 }$$

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Solution Steps

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}.

$$\sqrt{5}+2\times 3\sqrt{5}-3\sqrt{125}=-8\sqrt{5}$$

Multiply 2 and 3 to get 6.

$$\sqrt{5}+6\sqrt{5}-3\sqrt{125}=-8\sqrt{5}$$

Combine \sqrt{5} and 6\sqrt{5} to get 7\sqrt{5}.

$$7\sqrt{5}-3\sqrt{125}=-8\sqrt{5}$$

Factor 125=5^{2}\times 5. Rewrite the square root of the product \sqrt{5^{2}\times 5} as the product of square roots \sqrt{5^{2}}\sqrt{5}. Take the square root of 5^{2}.

$$7\sqrt{5}-3\times 5\sqrt{5}=-8\sqrt{5}$$

Multiply -3 and 5 to get -15.

$$7\sqrt{5}-15\sqrt{5}=-8\sqrt{5}$$

Combine 7\sqrt{5} and -15\sqrt{5} to get -8\sqrt{5}.

$$-8\sqrt{5}=-8\sqrt{5}$$

Add 8\sqrt{5} to both sides.

$$-8\sqrt{5}+8\sqrt{5}=0$$

Combine -8\sqrt{5} and 8\sqrt{5} to get 0.

$$0=0$$

Compare 0 and 0.

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