Question

find the cabe root of 512​

Answer 1

Answer:

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8

Step-by-step explanation:

sᴛᴇᴘ 1 : Find the prime factors of 512

512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

sᴛᴇᴘ 2 : Pair the factors of 512 in a group of three, such that they form cubes.

512 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2)

512 = 23 × 23 × 23

Using the law of exponent, we get;

512 = 29 [am.an = (a)m+n]

Or

512 = (23)3 [(am)n = amn]

512 = 83

sᴛᴇᴘ 3 : Now, we will apply cube root on both the sides to take out the factor (in cubes) as a single term.

3√512 = 3√(83)

So, here the cube root is eliminated by the cube of 8.

Hence, 3√512 = 8.