Solve 6sqrt{63}+7sqrt{28}-11sqrt{7}

$$6 \sqrt { 63 } + 7 \sqrt { 28 } - 11 \sqrt { 7 }$$

Evaluate

$$21\sqrt{7}\approx 55.560777532$$

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}.

$$6\times 3\sqrt{7}+7\sqrt{28}-11\sqrt{7}$$

Multiply 6 and 3 to get 18.

$$18\sqrt{7}+7\sqrt{28}-11\sqrt{7}$$

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}.

$$18\sqrt{7}+7\times 2\sqrt{7}-11\sqrt{7}$$

Multiply 7 and 2 to get 14.

$$18\sqrt{7}+14\sqrt{7}-11\sqrt{7}$$

Combine 18\sqrt{7} and 14\sqrt{7} to get 32\sqrt{7}.

$$32\sqrt{7}-11\sqrt{7}$$

Combine 32\sqrt{7} and -11\sqrt{7} to get 21\sqrt{7}.

$$21\sqrt{7}$$