Question

by what least number should 9720 be multiplied to get a perfect cube
a 15
b 25
c 5
d 75​

Answer 1

Answer:

B)75 is the correct answer.

Step-by-step explanation:

First,in order to find 9720 is a perfect cube,we should find the factors of 9720.

9720=2×2×2×3×3×3×3×3×5

=2³×3³×3²×5¹

Here 0ne 3 and two 5 should be multiplied.

That is 3×5²=75

Therefore,75 should be multiplied to 9720 to make it a perfect cube.

Hope it helps you.

Answer 2

75 is the least number should 9720 be multiplied to get a perfect cube [ The correct option is d. 75 ]

Given :

The number 9720

To find :

The least number should 9720 be multiplied to get a perfect cube is

a. 15

b. 25

c. 5

d. 75

Concept :

Step : I Firstly express the given number as a product of prime factor by using prime factorisation

Step : II Group the factors in triple form .

Step : III Take one factor from each pair.

Step : IV If no factor is left over in grouping (triples) then the number is perfect cube otherwise not

Solution :

Step 1 of 3 :

Write down the given number

Here the given number is 9720

Step 2 of 3 :

Factorise the given number

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{2}}}&{\underline{\sf{\:\:9720 \:\:}}}\\ {\underline{\sf{2}}}&\underline{\sf{\:\:4860 \:\:}} \\ {\underline{\sf{2}}}&\underline{\sf{\:\:2430 \:\:}} \\\underline{\sf{3}}&\underline{\sf{\:\:1215\:\:}}\\ {\underline{\sf{3}}}&\underline{\sf{\:\:405 \:\:}} \\ {\underline{\sf{3}}}&\underline{\sf{\:\:135 \:\:}} \\\underline{\sf{3}}&\underline{\sf{\:\:45\:\:}}\\\underline{\sf{3}}&\underline{\sf{\:\:15\:\:}}\\\underline{\sf{5}}&\underline{\sf{\:\:5\:\:}} \\\underline{\sf{}}&{\sf{\:\:1 \:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

9720

= 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 5

= 2³ × 3³ × 3² × 5

Step 3 of 3 :

Find the least number

We observe that there is no triplet for 3 and 5 in the above factorisation

So the number 9720 is not a perfect cube.

Now , 3 × 5 × 5 = 75

Therefore , 75 is the least number should 9720 be multiplied to get a perfect cube

Hence the correct option is d. 75

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