Solve this using surds rule √12/121
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To solve $\sqrt{\frac{12}{121}}$ using surds rules, we will simplify the numerator and the denominator separately.
Step 1: Apply the surd rule $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$.
$$ \sqrt{\frac{12}{121}} = \frac{\sqrt{12}}{\sqrt{121}} $$
Step 2: Simplify the numerator, $\sqrt{12}$.
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.
$$ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} $$
Step 3: Simplify the denominator, $\sqrt{121}$.
$$ \sqrt{121} = 11 $$
Step 4: Substitute the simplified numerator and denominator back into the fraction.
$$ \frac{\sqrt{12}}{\sqrt{121}} = \frac{2\sqrt{3}}{11} $$
The simplified form is:
$$ \boxed{\frac{2\sqrt{3}}{11}} $$
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