Find the cube root of 5832 by prime factorization method.
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Find the cube root of 5832 by prime factorization method.
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Answer:
the cube root of the given number 5832 is 18
Step-by-step explanation:
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Step-by-step explanation:
Therefore, the prime factors of 5832 are 2 and 3; and the product can be expressed as 5832=2×2×2×3×3×3×3×3×3=23×36
We know that m−−√3=(m)13
So the cube root of 5832 will be expressed as 5832−−−−√3 which is also written as (5832)13
Therefore, we get:
⇒(5832)13=(23×36)13
Since we know that the exponents are distributive over the multiplication, we get:
⇒(5832)13=(23×36)13=23×13×36×13
Now the expression in the powers can be easily solved as:
⇒(5832)13=23×13×36×13=21×32
Therefore, we get the value for cube root as 5832−−−−√3=2×32=2×9=18
Hence, the cube root of the given number 5832 is 18 .