What is the 4th roots of 81,and the cube roots of 125

Mathematics

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2 parts
a

3 and −33 \text{ and } -3

b
5

Step-by-step solution

7 steps

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Part a· 4 steps

To find the 4th roots of 81

  1. We are looking for a number xx such that x4=81x^4 = 81.

  2. We know that 3×3×3×3=813 \times 3 \times 3 \times 3 = 81.

    So, 34=813^4 = 81.

  3. We also know that (−3)×(−3)×(−3)×(−3)=81(-3) \times (-3) \times (-3) \times (-3) = 81.

    So, (−3)4=81(-3)^4 = 81.

  4. Therefore, the 4th roots of 81 are 3 and -3.

    The 4th roots of 81 are 3 and −3\boxed{3 \text{ and } -3}.

Part b5

To find the cube root of 125

  1. We are looking for a number yy such that y3=125y^3 = 125.

  2. We know that 5×5×5=1255 \times 5 \times 5 = 125.

    So, 53=1255^3 = 125.

  3. Therefore, the cube root of 125 is 5.

    The cube root of 125 is 5\boxed{5}.

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