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Find the cube root of the following number by prime factorisation method: 21952

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Detailed Solution

First, let’s take the smallest prime number i.e. 2:

\frac{21952}{2} = 10976

since it is divided exactly by 2 , we have 2 as one of the factors.
Moving further, let ‘s keep dividing it by 2 :

\frac{10976}{2} = 5488 \Rightarrow 2

\frac{5488}{2} = 2744 \Rightarrow 2

\frac{2744}{2} = 1372 \Rightarrow 2

\frac{1372}{2} = 686 \Rightarrow 2

\frac{686}{2} = 343 \Rightarrow 2

Now, let’s try a higher prime number that is 7 :

\frac{343}{7} = 49 \Rightarrow 7

\frac{49}{7} = 7 \Rightarrow 7

\frac{7}{7} = 1 \Rightarrow 7

Since it can’t be divided further, we got all the prime factors of the given number that is: 21952
Therefore

: 21952 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 7 \times 7 \times 7 .

For finding cube root, we will make a group of 3 same prime factors:

21952 = {(2)}^{3} \times {(2)}^{3} \times {(7)}^{3}

21952 = {(28)}^{3}

\sqrt[3]{21952} = 28 .

Therefore, the cube root of 21952 is 28.

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