Question

find the smallest number by which 3645 must be multiplied to get a perfect square​

Answer 1

Answer:

The required smallest number by which 3645 must be multiplied to get a perfect square is 5.

Step-by-step explanation:

To find : The smallest number by which 3645 must be multiplied to get a perfect square?

Solution :

First we factor the 3645

3 | 3645

3 | 1215

3 | 405

3 | 135

3 | 45

3 | 15

5 | 5

| 1

3645=3\times3 \times 3 \times 3 \times 3 \times3 \times 53645=3×3×3×3×3×3×5

3645=3^2 \times 3^2 \times 3^2 \times 53645=3

2

×3

2

×3

2

×5

If we pair of 2, 3 has 3 pairs and 5 is left alone.

So, If 5 is multiplied to the number then the number form is the perfect square.

Multiply both side by 5,

3645\times 5=3^2 \times 3^2 \times 3^2 \times 5^23645×5=3

2

×3

2

×3

2

×5

2

18225=(3\times 3 \times 3\times 5)^218225=(3×3×3×5)

2

18225=(135)^218225=(135)

2

Therefore, The required smallest number by which 3645 must be multiplied to get a perfect square is 5.

Step-by-step explanation:

This is the detailed answer...

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