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Find out the cube root of 216.

A. 5

B. 6

C. 7

D. 8

367.8k+ views

Hint:  Whenever you come across this kind of question, find out the prime factors of the given number and always assume the three time repeating digit as one and multiply them to get the cube root of the number.

In mathematics a cube root of a number x is number y such that ${y^3} = x$ ---(1)

Now finding the cube root of the number by prime factorization method.

From the equation (1)

${y^3} = 216$

$y = \sqrt[3]{{216}}$

Prime factors of 216 are

$216 = 2 \times {\text{2}} \times {\text{2}} \times {\text{3}} \times {\text{3}} \times {\text{3}}$

Now assume three time repeating digits are one as here by assuming each three as one we will get 2 and 3  

Now we should multiply these numbers.

 ${\text{2}} \times {\text{3 = 6 }}$

 $\sqrt[3]{{216}} = 6$, which is the cube root of 216 as mentioned.

So, Option B is correct.

NOTE: When you come across these kinds of questions, you can see the units place of the given number and since we have 6 in our units place of 216 you’ll get the cube root of the number as 6. Another example is, if we have to find out the cube root of 64 it turns out to be 4 as we have 4 in the units place.

Last updated date: 18th Sep 2023
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