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.
3675
Advertisements
उत्तर
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
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:
4761
Which of the following numbers are perfect square?
11
Which of the following numbers are perfect square?
32
Which of the following numbers are perfect square?
50
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.
The square number of 2 is _______________________
These number of boxes is equal to one square number. The number is _______________
Let x and y be natural numbers. If x divides y, then x3 divides y3.
A king wanted to reward his advisor, a wise man of the kingdom. So he asked the wiseman to name his own reward. The wiseman thanked the king but said that he would ask only for some gold coins each day for a month. The coins were to be counted out in a pattern of one coin for the first day, 3 coins for the second day, 5 coins for the third day and so on for 30 days. Without making calculations, find how many coins will the advisor get in that month?
A three digit perfect square is such that if it is viewed upside down, the number seen is also a perfect square. What is the number?
(Hint: The digits 1, 0 and 8 stay the same when viewed upside down, whereas 9 becomes 6 and 6 becomes 9.)
