Solve sqrt{162}-sqrt{588}+sqrt{450}

$$\sqrt { 162 } - \sqrt { 588 } + \sqrt { 450 }$$

Evaluate

$$24\sqrt{2}-14\sqrt{3}\approx 9.692414191$$

Solution Steps

Factor 162=9^{2}\times 2. Rewrite the square root of the product \sqrt{9^{2}\times 2} as the product of square roots \sqrt{9^{2}}\sqrt{2}. Take the square root of 9^{2}.

$$9\sqrt{2}-\sqrt{588}+\sqrt{450}$$

Factor 588=14^{2}\times 3. Rewrite the square root of the product \sqrt{14^{2}\times 3} as the product of square roots \sqrt{14^{2}}\sqrt{3}. Take the square root of 14^{2}.

$$9\sqrt{2}-14\sqrt{3}+\sqrt{450}$$

Factor 450=15^{2}\times 2. Rewrite the square root of the product \sqrt{15^{2}\times 2} as the product of square roots \sqrt{15^{2}}\sqrt{2}. Take the square root of 15^{2}.

$$9\sqrt{2}-14\sqrt{3}+15\sqrt{2}$$

Combine 9\sqrt{2} and 15\sqrt{2} to get 24\sqrt{2}.

$$24\sqrt{2}-14\sqrt{3}$$