Question

What is the smallest natural number by which 2304 should be multiplied so that the number is a perfect square. Also what is the number whose cube is so obtained?

Answer 1

Answer:

3

Step-by-step explanation:

2304*3=6912

sq root of 6912=144

12*12=144

Answer 2

$\huge{ \pink{\bigstar{\underline{\underline{Answer}}}}}$

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$\implies$Do prime factorization of 2304.

2|2304

2|1522

2|576

2|288

2|144

2|72

2|36

2|18

3|9

3|3

1

2304= $\sf 2 \times 2 \times 2 ,2 \times 2 \times 2 , 2 \times 2 \times \textcircled{\sf\footnotesize 2} , 3 \times 3\times \textcircled{\sf \footnotesize 3}$

So to make 2304 a perfect cube we need one more 2 and one more 3.

2 × 3 = 6

2304 × 6 = 13824

Now to check that 13824, do factorization

2|13824

2|6912

2|3456

2|1728

2|864

2|432

2|216

2|108

2|54

3|27

3|9

3|3

1

13824= 2×2×2, 2×2×2, 2×2×2, 3×3×3

$\implies \large{ \red{ \sf{\sqrt[3]{13824} = 24}}}$

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