Question

find the smallest numbers by which 2400 is to get multiplied to get perfect square and also find the square root of resulting number​

Answer 1

Required Solution:

Here, we have to find the smallest numbers by which 2400 is to get multiplied to get perfect square.

So, to solve this let us resolve the given number and the number that will remain unpaired will be the number that must be get multiplied to get perfect square.

→ Resolving 2400 in prime factors:

2 | 2400

2 | 1200

2 | 600

2 | 300

2 | 150

3 | 75

5 | 25

5 | 5

    | 1

We get that,

→ 2400 = 2 × 2 × 2 × 2 × 2 × 3 × 5 × 5

→ 2400 = 2² × 2² × 6 × 5²

Therefore, to get a perfect square number the given number should be multiplied by 6.

_________________

Now in the second part of the question, we are asked to find square root of the resulting number.

→ Resulting number = 2 × 2 × 2 × 2 × 6 × 6 × 5 × 5

→ Resulting number = 14,400

$\maltese$ Square root of the resulting number:

→ √14,400 = ?

So, again resolve the number in prime factors:

4 | 14400

4 | 3600

3 | 900

3 | 300

10 | 100

10 | 10

     | 1

Therefore, we get that:

• 14400 = 4 × 4 × 3 × 3 × 10 × 10

→ √14400 = 4 × 3 × 10

→ √14400 = 12 × 10

→ √14400 = 120

Therefore, square root of the resulting number (14400) is 120.