Solve this using surds rule √12/121

Mathematics

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Answer

2311\frac{2\sqrt{3}}{11}

Step-by-step solution

4 steps

To solve 12121\sqrt{\frac{12}{121}} using surds rules, we will simplify the numerator and the denominator separately.

  1. Apply the surd rule ab=ab\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}.

    12121=12121\sqrt{\frac{12}{121}} = \frac{\sqrt{12}}{\sqrt{121}}
  2. Simplify the numerator, 12\sqrt{12}.

    Find the largest perfect square factor of 12. The factors of 12 are 1, 2, 3, 4, 6, 12. The largest perfect square factor is 4.

    12=4×3=4×3=23\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}
  3. Simplify the denominator, 121\sqrt{121}.

    121=11\sqrt{121} = 11
  4. Substitute the simplified numerator and denominator back into the fraction.

    12121=2311\frac{\sqrt{12}}{\sqrt{121}} = \frac{2\sqrt{3}}{11}

    The simplified form is:

    2311\frac{2\sqrt{3}}{11}
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