find the cube root of 216 bye factorization method.
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find the cube root of 216 bye factorization method.
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Cube root of 216=
=2×3=6
So cuve root of 216 is 6
Answer:
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6
Step-by-step explanation:
sᴛᴇᴘ 1: Find the prime factors of 216
216 = 2 × 2 × 2 × 3 × 3 × 3
sᴛᴇᴘ 2 : Clearly, 216 is a perfect cube. Therefore, group the factors of 216 in a pair of three and write in the form of cubes.
216 = (2 × 2 × 2) × (3 × 3 × 3)
216 = 23 × 33
Using the law of exponent, we get;
216 = 63 [ambm = (ab)m]
sᴛᴇᴘ 3 : Now, we will apply cube root on both the sides to take out the factor as a single term, which is in cubes.
3√216 = 3√(63)
So, here the cube root is cancelled by the cube of 6.
Hence, 3√216 = 6