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For the cube root of 216, which is written as [3]216. This means we need to find a number that, when multiplied by itself three times, equals 216.

Biology

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Answer

6

Step-by-step solution

4 steps

  1. Identify the operation.

    The problem asks for the cube root of 216, which is written as 2163\sqrt[3]{216}. This means we need to find a number that, when multiplied by itself three times, equals 216.

  2. Find the prime factorization of 216.

    216=2×108216 = 2 \times 108 108=2×54108 = 2 \times 54 54=2×2754 = 2 \times 27 27=3×927 = 3 \times 9 9=3×39 = 3 \times 3

    So, the prime factorization of 216 is 2×2×2×3×3×32 \times 2 \times 2 \times 3 \times 3 \times 3.

  3. Group the prime factors into sets of three.

    216=(2×2×2)×(3×3×3)216 = (2 \times 2 \times 2) \times (3 \times 3 \times 3) 216=23×33216 = 2^3 \times 3^3

  4. Calculate the cube root.

    2163=23×333\sqrt[3]{216} = \sqrt[3]{2^3 \times 3^3}

    Using the property ann=a\sqrt[n]{a^n} = a:

    23×333=233×333\sqrt[3]{2^3 \times 3^3} = \sqrt[3]{2^3} \times \sqrt[3]{3^3} =2×3= 2 \times 3 =6= 6

    The cube root of 216 is 6.

    66
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