Solve 4sqrt{28}-sqrt{18}+2sqrt{98}-7sqrt{63}

$$4 \sqrt { 28 } - \sqrt { 18 } + 2 \sqrt { 98 } - 7 \sqrt { 63 }$$

Evaluate

$$11\sqrt{2}-13\sqrt{7}\approx -18.838417858$$

Solution Steps

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}.

$$4\times 2\sqrt{7}-\sqrt{18}+2\sqrt{98}-7\sqrt{63}$$

Multiply 4 and 2 to get 8.

$$8\sqrt{7}-\sqrt{18}+2\sqrt{98}-7\sqrt{63}$$

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}.

$$8\sqrt{7}-3\sqrt{2}+2\sqrt{98}-7\sqrt{63}$$

Factor 98=7^{2}\times 2. Rewrite the square root of the product \sqrt{7^{2}\times 2} as the product of square roots \sqrt{7^{2}}\sqrt{2}. Take the square root of 7^{2}.

$$8\sqrt{7}-3\sqrt{2}+2\times 7\sqrt{2}-7\sqrt{63}$$

Multiply 2 and 7 to get 14.

$$8\sqrt{7}-3\sqrt{2}+14\sqrt{2}-7\sqrt{63}$$

Combine -3\sqrt{2} and 14\sqrt{2} to get 11\sqrt{2}.

$$8\sqrt{7}+11\sqrt{2}-7\sqrt{63}$$

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}.

$$8\sqrt{7}+11\sqrt{2}-7\times 3\sqrt{7}$$

Multiply -7 and 3 to get -21.

$$8\sqrt{7}+11\sqrt{2}-21\sqrt{7}$$

Combine 8\sqrt{7} and -21\sqrt{7} to get -13\sqrt{7}.

$$-13\sqrt{7}+11\sqrt{2}$$