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Q.

The cube root of 4096 is ____.


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Detailed Solution

The cube root of 4096 is 16.
The given number is 4096.
Find prime factors of 4096.
4096=2×2×2×2×2×2×2×2×2×2×2×2 ⇒4096= 2×2×2 ¯ × 2×2×2 ¯ × 2×2×2 ¯ × 2×2×2 ¯ ⇒ 4096 3 = 2×2×2 ¯ 3 × 2×2×2 ¯ 3 × 2×2×2 ¯ 3 × 2×2×2 ¯ 3 ⇒ 4096 3 = 2 3 3 × 2 3 3 × 2 3 3 × 2 3 3 ⇒ 4096 3 =2×2×2×2 ⇒ 4096 3 =16 Therefore, the cube root of 4096 is 16.
 
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