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Find the cube root of 474552.

Answer
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Hint: Proceed the solution of this question by doing prime factor of given number then try to form triplets of prime numbers, if we get triplets of all prime numbers then it will be a perfect cube and multiplication of all prime numbers will be our cube root.

Complete step-by-step answer:

We know that
The process of cubing is similar to squaring, only that the number is multiplied three times instead of two. The exponent used for cubes is 3. for examples are 8³ = 8*8*8 = 512.

In prime factorisation-
We will find prime factors of 474552, if it is a perfect cube and then will pair them in a group of three.
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⇒ So, the prime factors of 474552=2×2×2×3×3×3×13×13×13
⇒ 474552 = 23×33×133
Since 2, 3 and 13 occurs in triplets
474552 is a perfect cube
On taking cube root on both side
⇒ 474552 = 23×33×133
It can be write like,
 474552=(2×3×13)3
On taking cube root on both side
4745523=(2×3×13)33
Cube root can be write raised to power 13
4745523=(2×3×13)3×13

On cancelling exponential power
4745523=(2×3×13)1
⇒ So cube root of 474552 ​= 2×3×13=78

Note: We should know that the cubic function is a one-to-one function. This is because cubing a negative number results in an answer different to that of cubing its positive counterpart. We can say this because when three negative numbers are multiplied together, two of the negatives are cancelled but one remains, so the result is also negative. 8³ = 8*8*8 = 512 and (-8) ³ = (-8) *(-8) *(-8) = -512.
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