Solve =sqrt{45}+sqrt{41}+sqrt{50}

$$= \sqrt { 45 } + \sqrt { 41 } + \sqrt { 50 }$$

Evaluate

$$\sqrt{41}+3\sqrt{5}+5\sqrt{2}\approx 20.182395982$$

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}.

$$3\sqrt{5}+\sqrt{41}+\sqrt{50}$$

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}.

$$3\sqrt{5}+\sqrt{41}+5\sqrt{2}$$