Question

Find the length of the side of asquare field whose area is
31. Find cube root of 438976 using prime factorization.
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Answer 1

Answer:

Step-by-step explanation:

We have the number 438976.

2|438976

2|219488

2|109744

2|54872

2|27436

2|13718

19|6859

19|361

19|19

|1

Divide 438976 by prime number 2 until we get 6859.

Then number 6859 is divisible by 19 and thus we get 1.

∴438976 = 2 × 2 × 2 × 2 × 2 × 2 × 19 × 19 × 19

438976 = 2^3 × 2^3 × 19^3

Now, by taking the cube root on both RHS and LHS

3√438976 = √2^3 × 2^3 × 19^3

3√438976 = 2 × 2 × 19 = 76

∴ The cube root of 438976 = 76 by prime factorization.

Note: Another way is to find the cubes of the options provided

a)  74^3 = 405224

b)  72^3 = 373248

c)  76^3 = 438976

d)  71^3 = 357911