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\sqrt{63}
Rewrite the division of square roots \frac{\sqrt{126}}{\sqrt{2}} as the square root of the division \sqrt{\frac{126}{2}} and perform the division.
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}.