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.
2880
Solution
2880 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 5
Grouping them into pairs of equal factors:
2880 = (2 x 2) x (2 x 2) x (2 x 2) x (3 x 3) x 5
There is a 5 as the leftover. For a number to be a perfect square, each prime factor has to be paired. Hence, 2880 must be multiplied by 5 to be a perfect square.
The new number would be (2 x 2) x (2 x 2) x (2 x 2) x (3 x 3) x (5 x 5).
Furthermore, we have:
(2 x 2) x (2 x 2) x (2 x 2) x (3 x 3) x (5 x 5) = (2 x 2 x 2 x 3 x 5) x (2 x 2 x 2 x 3 x 5)
Hence, the number whose square is the new number is:
2 x 2 x 2 x 3 x 5 = 120
APPEARS IN
RELATED QUESTIONS
Which of the following numbers are perfect squares?
2500
Show that each of the following numbers is a perfect square. Also, find the number whose square is the given number in each case:
1156
Which of the following numbers are perfect square?
12
By what numbers should each of the following be divided to get a perfect square ? Also, find the number whose square is the new number.
16562
Find the smallest number by which 1152 must be divided so that it becomes a perfect square. Also, find the number whose square is the resulting number.
The following number are not perfect squares. Give reason.
1547
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?
The square of 0.7 is ______.
The square of every natural number is always greater than the number itself.
