Advertisements
Advertisements
Question
By what number should each of the following numbers be multiplied to get a perfect square ? Also, find the number whose square is the new number.
3675
Advertisements
Solution
3675 = 3 x 5 x 5 x 7 x 7
Grouping them into pairs of equal factors:
3675 = (5 x 5) x (7 x 7) x 3
The factor, 3 is not paired. For a number to be a perfect square, each prime factor has to be paired. Hence, 3675 must be multiplied by 3 for it to be a perfect square.
The new number would be (5 x 5) x (7 x 7) x (3 x 3).
Furthermore, we have:
(5 x 5) x (7 x 7) x (3 x 3) = (3 x 5 x 7) x (3 x 5 x 7)
Hence, the number whose square is the new number is:
3 x 5 x 7 = 105
APPEARS IN
RELATED QUESTIONS
Show that each of the following numbers is a perfect square. Also, find the number whose square is the given number in each case:
4761
Which of the following numbers are perfect square?
32
Which of the following numbers are perfect square?
79
By what number should each of the following numbers be multiplied to get a perfect square? Also, find the number whose square is the new number.
605
Find the least number of three digits which is perfect square.
The following number are not perfect squares. Give reason.
1547
The following number is not perfect square. Give reason.
45743
Show that the following number is not perfect square:
743522
There is a large square portrait of a leader that covers an area of 4489 cm2. If each side has a 2 cm liner, what would be its area?
There are ______ perfect squares between 1 and 100.
