Question

find the smallest number by which 2400 is to be multiplied to get perfect square and also find the squars root of theresulting number

Answer 1

hope this helps...........^-^

Answer 2

Answer:

The smallest number by which 2400 is to be multiplied to get perfect square is 6 and the square root of the resulting number is 120

Step-by-step explanation:

Given: Number = 2400

To Find : Find the smallest number by which 2400 is to be multiplied to get perfect square and also find the square root of the resulting number

Solution:

Number = 2400

Prime factorization of 2400 

    2 |2400

       |_________

    2 |1200    

       |_________

    2 | 600

       |_________

    2 | 300

       |_________

    2 | 150

       |_________

    3 |  75

       |_________

    5 |  25

       |_________

    5 |   5

       |_________

       |   1

$2400=2 \times 2 \times 2\times 2 \times 2 \times 3 \times 5 \times 5$

$2400=2^2 \times 2^2 \times 2 \times 3 \times 5^2$

$3 \times 2 =6$

So, 6 is the least number which should be multiplied to get perfect square

So, the resulting number is $2400 \times 6 =14400$

So, $\sqrt{14400}=120$

Hence  the smallest number by which 2400 is to be multiplied to get perfect square is 6 and the square root of the resulting number is 120