Solve 5sqrt{63}+3sqrt{2}-2sqrt{18}+3sqrt{7}+3sqrt{72}-sqrt{28}

$$5 \sqrt { 63 } + 3 \sqrt { 2 } - 2 \sqrt { 18 } + 3 \sqrt { 7 } + 3 \sqrt { 72 } - \sqrt { 28 }$$

Evaluate

$$15\sqrt{2}+16\sqrt{7}\approx 63.545224413$$

Solution Steps

Factor 63=3^{2}\times 7. Rewrite the square root of the product \sqrt{3^{2}\times 7} as the product of square roots \sqrt{3^{2}}\sqrt{7}. Take the square root of 3^{2}.

$$5\times 3\sqrt{7}+3\sqrt{2}-2\sqrt{18}+3\sqrt{7}+3\sqrt{72}-\sqrt{28}$$

Multiply 5 and 3 to get 15.

$$15\sqrt{7}+3\sqrt{2}-2\sqrt{18}+3\sqrt{7}+3\sqrt{72}-\sqrt{28}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$15\sqrt{7}+3\sqrt{2}-2\times 3\sqrt{2}+3\sqrt{7}+3\sqrt{72}-\sqrt{28}$$

Multiply -2 and 3 to get -6.

$$15\sqrt{7}+3\sqrt{2}-6\sqrt{2}+3\sqrt{7}+3\sqrt{72}-\sqrt{28}$$

Combine 3\sqrt{2} and -6\sqrt{2} to get -3\sqrt{2}.

$$15\sqrt{7}-3\sqrt{2}+3\sqrt{7}+3\sqrt{72}-\sqrt{28}$$

Combine 15\sqrt{7} and 3\sqrt{7} to get 18\sqrt{7}.

$$18\sqrt{7}-3\sqrt{2}+3\sqrt{72}-\sqrt{28}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$18\sqrt{7}-3\sqrt{2}+3\times 6\sqrt{2}-\sqrt{28}$$

Multiply 3 and 6 to get 18.

$$18\sqrt{7}-3\sqrt{2}+18\sqrt{2}-\sqrt{28}$$

Combine -3\sqrt{2} and 18\sqrt{2} to get 15\sqrt{2}.

$$18\sqrt{7}+15\sqrt{2}-\sqrt{28}$$

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$18\sqrt{7}+15\sqrt{2}-2\sqrt{7}$$

Combine 18\sqrt{7} and -2\sqrt{7} to get 16\sqrt{7}.

$$16\sqrt{7}+15\sqrt{2}$$