Question

Find the smallest number by which each given numbers must be multiplied so that the product is a cube number 15125

Answer 1

Answer:

11 should be multiplied

Step-by-step explanation:

15,125 = 5 × 5 × 5 × 11 × 11

15125 should be multiplied with 11 to get a perfect cube

15,125 × 11 = 166375

166375 is perfect cube of 55

55 × 55 × 55 = 166375

hope you get your answer

Answer 2

The smallest number is 11 by which 15125 must be multiplied so that the product is a cube number

Given :

The number 15125

To find :

The smallest number by which 15125 must be multiplied so that the product is a cube number

Solution :

Step 1 of 3 :

Write down the given number

Here the given number is 15125

Step 2 of 3 :

Check 15125 is a perfect cube or not

$\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{5}}}&{\underline{\sf{\:\:15125 \:\:}}}\\ {\underline{\sf{5}}}&\underline{\sf{\:\:3025 \:\:}} \\ {\underline{\sf{5}}}&\underline{\sf{\:\:605 \:\:}} \\\underline{\sf{11}}&\underline{\sf{\:\:121\:\:}}\\\underline{\sf{11}}&\underline{\sf{\:\:11\:\:}} \\ {\underline{\sf{}}}&\underline{\sf{\:\:1\:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}$

Prime factorisation of 15125 gives

15125 = 5 × 5 × 5 × 11 × 11

∴ 15125 = 5³ × 11²

After grouping the factors in triple form we see that the factor 11 is left over in grouping (triples)

So the number is 15125 is not perfect cube

Step 3 of 3 :

Find the required number

Since the factor 11 is left over in grouping (triples)

So we need to multiply the number 15125 with 11 so that the obtained number 166375 is a perfect cube.

In addition the cube root of 166375

$\displaystyle \sf{ = \sqrt[3]{ {5}^{3} \times {11}^{3} } }$

$\displaystyle \sf{ = 5 \times 11}$

$\displaystyle \sf{ = 55 }$

Hence the smallest number is 11 by which 15125 must be multiplied so that the product is a cube number

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