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Q.

The cube root of  125 216 is ____.


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Detailed Solution

The cube root of  125 216 is 5 6 .
The given number is 125 216 .
Find prime factors of 125 216 .
125 216 3 = 5×5×5 2×2×2×3×3×3 3
Make three groups of factors.
5×5×5 2×2×2×3×3×3 3 = 5 2×3 5 2×3 5 2×3 3 = 5 2×3 3 3
Simplify to get the cube root.
125 216 3 = 5 2×3 3 3 = 5 6 3 3 = 5 6
∴ 125 216 3 = 5 6
Thus, the cube root of 125 216 is 5 6 .
 
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