Discussion
Find the value of \( \sqrt{0.0169} \).
Answer: B
Correct answer: 0.13
A square root halves the number of decimal places, and \( \sqrt{169} = 13 \). Since 0.0169 has four decimal places, the root has two: \[ \sqrt{0.0169} = 0.13. \] Written as a fraction the reasoning is plain: \[ \sqrt{0.0169} = \sqrt{\frac{169}{10000}} = \frac{13}{100} = 0.13. \] Checking is immediate: \( 0.13 \times 0.13 = 0.0169 \). The rule requires an even number of decimal places for the root to terminate, which is why such questions always supply two, four or six. A cube root divides the places by three instead, so \( \sqrt[3]{0.000027} = 0.03 \). The perfect squares up to 30 are worth knowing by heart, since almost every question of this kind is built on one: 121, 144, 169, 196, 225, 256, 289, 324, 361, 400.
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