Solve 2sqrt{45}-2sqrt{54}+2sqrt{5}

$$2 \sqrt { 45 } - 2 \sqrt { 54 } + 2 \sqrt { 5 }$$

Evaluate

$$8\sqrt{5}-6\sqrt{6}\approx 3.191605363$$

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}.

$$2\times 3\sqrt{5}-2\sqrt{54}+2\sqrt{5}$$

Multiply 2 and 3 to get 6.

$$6\sqrt{5}-2\sqrt{54}+2\sqrt{5}$$

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$6\sqrt{5}-2\times 3\sqrt{6}+2\sqrt{5}$$

Multiply -2 and 3 to get -6.

$$6\sqrt{5}-6\sqrt{6}+2\sqrt{5}$$

Combine 6\sqrt{5} and 2\sqrt{5} to get 8\sqrt{5}.

$$8\sqrt{5}-6\sqrt{6}$$

Factor

$$2 {(4 \sqrt{5} - 3 \sqrt{6})} = 3.191605363$$