Solve 15sqrt{20}-02sqrt{45b^7}+5sqrt{500}-08sqrt{80b^7}

$$15 \sqrt { 20 } - 02 \sqrt { 45 b ^ { 7 } } + 5 \sqrt { 500 } - 08 \sqrt { 80 b ^ { 7 } }$$

Evaluate

$$80\sqrt{5}\approx 178.8854382$$

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}.

$$15\times 2\sqrt{5}-0\times 2\sqrt{45b^{7}}+5\sqrt{500}-0\times 8\sqrt{80b^{7}}$$

Multiply 15 and 2 to get 30.

$$30\sqrt{5}-0\times 2\sqrt{45b^{7}}+5\sqrt{500}-0\times 8\sqrt{80b^{7}}$$

Multiply 0 and 2 to get 0.

$$30\sqrt{5}-0\sqrt{45b^{7}}+5\sqrt{500}-0\times 8\sqrt{80b^{7}}$$

Anything times zero gives zero.

$$30\sqrt{5}-0+5\sqrt{500}-0\times 8\sqrt{80b^{7}}$$

Factor 500=10^{2}\times 5. Rewrite the square root of the product \sqrt{10^{2}\times 5} as the product of square roots \sqrt{10^{2}}\sqrt{5}. Take the square root of 10^{2}.

$$30\sqrt{5}-0+5\times 10\sqrt{5}-0\times 8\sqrt{80b^{7}}$$

Multiply 5 and 10 to get 50.

$$30\sqrt{5}-0+50\sqrt{5}-0\times 8\sqrt{80b^{7}}$$

Multiply 0 and 8 to get 0.

$$30\sqrt{5}-0+50\sqrt{5}-0\sqrt{80b^{7}}$$

Anything times zero gives zero.

$$30\sqrt{5}-0+50\sqrt{5}-0$$

Multiply -1 and 0 to get 0.

$$30\sqrt{5}+0+50\sqrt{5}-0$$

Anything plus zero gives itself.

$$30\sqrt{5}+50\sqrt{5}-0$$

Combine 30\sqrt{5} and 50\sqrt{5} to get 80\sqrt{5}.

$$80\sqrt{5}-0$$

Multiply -1 and 0 to get 0.

$$80\sqrt{5}+0$$

Anything plus zero gives itself.

$$80\sqrt{5}$$