Solve 7sqrt{63}+sqrt{567}-2sqrt{112}

$$7 \sqrt { 63 } + \sqrt { 567 } - 2 \sqrt { 112 }$$

Evaluate

$$22\sqrt{7}\approx 58.206528843$$

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}.

$$7\times 3\sqrt{7}+\sqrt{567}-2\sqrt{112}$$

Multiply 7 and 3 to get 21.

$$21\sqrt{7}+\sqrt{567}-2\sqrt{112}$$

Factor 567=9^{2}\times 7. Rewrite the square root of the product \sqrt{9^{2}\times 7} as the product of square roots \sqrt{9^{2}}\sqrt{7}. Take the square root of 9^{2}.

$$21\sqrt{7}+9\sqrt{7}-2\sqrt{112}$$

Combine 21\sqrt{7} and 9\sqrt{7} to get 30\sqrt{7}.

$$30\sqrt{7}-2\sqrt{112}$$

Factor 112=4^{2}\times 7. Rewrite the square root of the product \sqrt{4^{2}\times 7} as the product of square roots \sqrt{4^{2}}\sqrt{7}. Take the square root of 4^{2}.

$$30\sqrt{7}-2\times 4\sqrt{7}$$

Multiply -2 and 4 to get -8.

$$30\sqrt{7}-8\sqrt{7}$$

Combine 30\sqrt{7} and -8\sqrt{7} to get 22\sqrt{7}.

$$22\sqrt{7}$$