Advertisements
Advertisements
प्रश्न
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.
1575
उत्तर
1575 = 3 x 3 x 5 x 5 x 7
Grouping them into pairs of equal factors:
1575 = (3 x 3) x (5 x 5) x 7
The factor, 7 is not paired. For a number to be a perfect square, each prime factor has to be paired. Hence, 1575 must be divided by 7 for it to be a perfect square.
The new number would be (3 x 3) x (5 x 5).
Furthermore, we have:
(3 x 3) x (5 x 5) = (3 x 5) x (3 x 5)
Hence, the number whose square is the new number is:
3 x 5 = 15
APPEARS IN
संबंधित प्रश्न
Using prime factorization method, find which of the following numbers are perfect square?
2916
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
The following number is not perfect square. Give reason.
45743
Show that the following number is not perfect square:
9327
Show that the following number is not perfect square:
4058
When a square number ends in 6, its square root will have 6 in the unit’s place
What is next square number of 49?
The square of every natural number is always greater than the number itself.
Find the side of a square whose area is equal to the area of a rectangle with sides 6.4 m and 2.5 m.
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?
