Solve 4sqrt{5}+sqrt{45}-sqrt{8}+4*sqrt{2}

$$4 \sqrt { 5 } + \sqrt { 45 } - \sqrt { 8 } + 4 \times \sqrt { 2 }$$

Evaluate

$$2\sqrt{2}+7\sqrt{5}\approx 18.480902967$$

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}.

$$4\sqrt{5}+3\sqrt{5}-\sqrt{8}+4\sqrt{2}$$

Combine 4\sqrt{5} and 3\sqrt{5} to get 7\sqrt{5}.

$$7\sqrt{5}-\sqrt{8}+4\sqrt{2}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$7\sqrt{5}-2\sqrt{2}+4\sqrt{2}$$

Combine -2\sqrt{2} and 4\sqrt{2} to get 2\sqrt{2}.

$$7\sqrt{5}+2\sqrt{2}$$