Question

1) Find the cube roots of the following numbers: (i) -5832
2) Find the cube root of each of the following: (i) -216 x 1728

Answer 1

Hey there !

Solution :

1. Find the cube roots of the following numbers :

( a ) - 5832

The cube root of any number can be found out using simple method called Prime Factorisation. So let us Prime Factorise the above number.

5832 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3

=> 5832 = 2³ × 3³ × 3³

Therefore ∛ 5832 = ∛ ( 2³ × 3³ × 3³ )

=> ∛ 5832 = 2 × 3 × 3 

=> ∛ 5832 = 6 × 3 = 18

Hence Cube Root of 5832 is 18. But the number in the question is negative, Hence the answer would be - 18.

That is, ( - 18 ) × ( - 18 ) × ( - 18 ) = - 5832.

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2. - 216 × 1728

Let us calculate the individual cube roots and later multiply to find the product's cube root.

Prime Factorisation of 216:

=>  216 = 2 × 2 × 2 × 3 × 3 × 3 

=>  216 = 2³ × 3³

=> ∛ 216 = ∛ ( 2³ × 3³ )

=> ∛ 216 = 2 × 3 = 6  

But the question has - 216, So it must be - 6³.


Prime Factorisation of 1728:

=> 1728 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 

=> 1728 = 2³ × 2³ × 3³

=> ∛ 1728 = ∛ ( 2³ × 2³ × 3³ )

=> ∛ 1728 = 2 × 2 × 3 = 12

Hence We got the respective values of - 216 and 1728. Hence multiplying their roots we get

=> - 6 × 12  = - 72

So we get the product to be - 72. Let us verify our answer. Calculating the values of the question we get,

=> - 216 × 1728 = - 373248

Taking Cube root of - 373248 we get answer as - 72.

Hence our answer is correct. Hence the cube root of the product of the equation - 216 × 1728 is equal to - 72.

Hope my answer helped :-)

Answer 2

Cube root of -5832 = -18


Cube root of -216 × 1728 = -72


On finding any mistake, comment immediately.