Solve 13sqrt{28}-2sqrt{63}-7sqrt{7}=

$$13 \sqrt { 28 } - 2 \sqrt { 63 } - 7 \sqrt { 7 } =$$

Evaluate

$$13\sqrt{7}\approx 34.394767044$$

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}.

$$13\times 2\sqrt{7}-2\sqrt{63}-7\sqrt{7}$$

Multiply 13 and 2 to get 26.

$$26\sqrt{7}-2\sqrt{63}-7\sqrt{7}$$

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}.

$$26\sqrt{7}-2\times 3\sqrt{7}-7\sqrt{7}$$

Multiply -2 and 3 to get -6.

$$26\sqrt{7}-6\sqrt{7}-7\sqrt{7}$$

Combine 26\sqrt{7} and -6\sqrt{7} to get 20\sqrt{7}.

$$20\sqrt{7}-7\sqrt{7}$$

Combine 20\sqrt{7} and -7\sqrt{7} to get 13\sqrt{7}.

$$13\sqrt{7}$$