Maharashtra BoardEnglish MediumSTD 8MathsCubes and Cube Roots4 Marks
Question
Find the cube root of the following rational numbers:
0.003375
✓
Answer
We have:
$0.003375=\frac{3375}{1000000}$
$\therefore\sqrt[3]{0.0003375}$
$=\sqrt[]{\frac{3375}{1000000}}$
$={\frac{\sqrt[3]{3375}}{\sqrt[3]{1000000}}}$
Now
On factorising 1728 into prime factors, we get:
3375 = 3 × 3 × 3 × 5 × 5 × 5
On grouping the factors in triples of equal factors, we get:
3375 = {3 × 3 × 3} × {5 × 5 × 5}
Now, taking one factor from each triple, we get:
$\sqrt[3]{3375}=3\times5=15$
Also
$\sqrt[3]{1000000}$
$\sqrt[3]{100\times100\times100}=100$
$\therefore\sqrt[3]{0.003375}$
$={\frac{\sqrt[3]{3375}}{\sqrt[3]{1000000}}}$
$\frac{15}{100}=0.15$
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