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614−4224\frac{6\sqrt{14} - \sqrt{42}}{24}

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Full solution

Q. 614−4224\frac{6\sqrt{14} - \sqrt{42}}{24}
  1. Factor out 14\sqrt{14}: Factor out 14\sqrt{14} from the numerator.\newline614−4224=14(6−3)24\frac{6\sqrt{14} - \sqrt{42}}{24} = \frac{\sqrt{14}(6 - \sqrt{3})}{24}
  2. Simplify 42\sqrt{42}: Simplify the square root of 4242.\newline42=14⋅3=14⋅3\sqrt{42} = \sqrt{14 \cdot 3} = \sqrt{14} \cdot \sqrt{3}
  3. Substitute 42\sqrt{42}: Substitute 42\sqrt{42} with 14⋅3\sqrt{14} \cdot \sqrt{3} in the numerator.\newline14(6−3)24=614−14324\frac{\sqrt{14}(6 - \sqrt{3})}{24} = \frac{6\sqrt{14} - \sqrt{14}\sqrt{3}}{24}
  4. Simplify fraction: Simplify the fraction by dividing the numerator and the denominator by 66. 614−14324=14(1−3/6)4\frac{6\sqrt{14} - \sqrt{14}\sqrt{3}}{24} = \frac{\sqrt{14}(1 - \sqrt{3}/6)}{4}

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