Solve 2sqrt{45}-sqrt{50}+3sqrt{75}

$$2 \sqrt { 45 } - \sqrt { 50 } + 3 \sqrt { 75 }$$

Evaluate

$$6\sqrt{5}+15\sqrt{3}-5\sqrt{2}\approx 32.326102167$$

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}.

$$2\times 3\sqrt{5}-\sqrt{50}+3\sqrt{75}$$

Multiply 2 and 3 to get 6.

$$6\sqrt{5}-\sqrt{50}+3\sqrt{75}$$

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$6\sqrt{5}-5\sqrt{2}+3\sqrt{75}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

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

Multiply 3 and 5 to get 15.

$$6\sqrt{5}-5\sqrt{2}+15\sqrt{3}$$