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4\sqrt{7}-3\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}.
\sqrt{7}
Combine 4\sqrt{7} and -3\sqrt{7} to get \sqrt{7}.