Advertisements
Advertisements
प्रश्न
Show that each of the following numbers is a perfect square. Also, find the numer whose square is the given number in each case:
2025
Advertisements
उत्तर
In problem, factorise the number into its prime factor.
2025 = 3 x 3 x 3 x 3 x 5 x 5
Grouping the factors into pairs of equal factors, we obtain:
2025 = (3 x 3) x (3 x 3) x (5 x 5)
No factors are left over. Hence, 2025 is a perfect square. Moreover, by grouping 2025 into equal factors:
2025 = (3 x 3 x 5) x (3 x 3 x 5)
= (3 x 3 x 5)2
Hence, 2025 is the square of 45, which is equal to 3 x 3 x 5.
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.
3468
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.
7776
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
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.
3698
Find the smallest number by which 28812 must be divided so that the quotient becomes a perfect square.
Show that the following number is not perfect square:
4058
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 ones digit in the square of 77 is ___________
The square root of 24025 will have ______ digits.
