Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
605 = 5 x 11 x 11
Grouping them into pairs of equal factors:
605 = 5 x (11 x 11)
The factor, 5 is not paired. For a number to be a perfect square, each prime factor has to be paired. Hence, 605 must be multiplied by 5 for it to be a perfect square.
The new number would be (5 x 5) x (11 x 11).
Furthermore, we have:
(5 x 5) x (11 x 11) = (5 x 11) x (5 x 11)
Hence, the number whose square is the new number is:
5 x 11 = 55
APPEARS IN
संबंधित प्रश्न
Show that each of the following numbers is a perfect square. Also, find the number whose square is the given number in each case:
14641
Using prime factorization method, find which of the following numbers are perfect square?
225
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.
3174
The following number is not perfect square. Give reason.
8948
13 and 31 is a strange pair of numbers such that their squares 169 and 961 are also mirror images of each other. Find two more such pairs.
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 number of 2 is _______________________
The square number of 5 is _________________________
Which of the following is a square of an even number?
The product of two perfect squares is a perfect square.
