Question

find the smallest number by which each of the given numbers must be multiplied so that the product a perfect square A) 240 , B) 432 ,C) 2592 , D) 18000, E) 21952

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Answer 1

Step-by-step explanation:

A) 240

240 = 2 × 2 × 2 × 2 × 3 × 5

multiply 240 with 15 to get a perfect square

240 × 15 = 3600

3600 is perfect square of 60

B) 432

432 = 2 × 2 × 2 × 2 × 3 × 3 × 3

multiply 432 with 3 to get a perfect square

432 × 3 = 1296

1296 is perfect square of 36

C) 2592

2,592 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3

multiply 2592 with 2 to get a perfect square

2592 × 2 = 5184

5184 is a perfect square of 72

D) 18000

18,000 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 × 5

multiply 18000 with 5 to get a perfect square

18000 × 5 = 90000

90000 is a perfect square of 300

E) 21952

21,952 = 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7 × 7

multiply 21952 with 7 to get a perfect square

21952 × 7 = 153,664

153664 is a perfect square of 392

hope you get your answer

Answer 2

Answer:

In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself.

Explanation:

(A) 240 = 2 × 2 × 2 × 2 × 3 × 5

Now we can see that here 2 is having pair while 3 and 5 are not getting their pair so 3×5=15 is the smallest number that should be multiplied to 240 to make it a perfect square.

(B) 432 = 2 × 2 × 2 × 2 × 3 × 3 × 3

Now we can see that here 2 is having pair while 3 is not getting its pair so 3 is the smallest number that should be multiplied to 432 to make it a perfect square.

(C) 2592 = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3

Now we can see that here 3 is having pair while 2 is not getting its pair so 2 is the smallest number that should be multiplied to 2592 to make it a perfect square.

(D) 18000 = 2 × 2 × 2 × 2 × 5 × 5 × 5 × 3 × 3

Now we can see that here 2 is having pair while 5 is not getting its pair so 5 is the smallest number that should be multiplied to 18000 to make it a perfect square.

(E) 21952 = 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7 × 7

Now we can see that here 2 is having pair while 7 is not getting its pair so 7 is the smallest number that should be multiplied to 21952 to make it a perfect square.