Advertisements
Advertisements
प्रश्न
Find the smallest number by which 3645 must be divided so that it becomes a perfect square. Also, find the square root of the resulting number.
Advertisements
उत्तर
The prime factorisation of 3645:
3645 = 3 x 3 x 3 x 3 x 3 x 3 x 5
Grouping the factors into pairs of equal factors, we get:
3645 = (3 x 3) x (3 x 3) x (3 x 3) x 5
The factor, 5 does not have a pair. Therefore, we must divide 3645 by 5 to make a perfect square. The new number is:
(3 x 3) x (3 x 3) x (3 x 3) = 729
Taking one factor from each pair on the LHS, the square root of the new number is 3 x 3 x 3, which is equal to 27.
APPEARS IN
संबंधित प्रश्न
For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.
1458
For the following number, find the smallest whole number by which it should be divided so as to get a perfect square number. Also find the square root of the square number so obtained.
2925
Find the smallest number by which the given number must bew multiplied so that the product is a perfect square:
7688
Find the square root the following by prime factorization.
7056
By splitting into prime factors, find the square root of 11025.
Find the smallest number by which 12748 be mutliplied so that the product is a perfect square?
Examine if the following is a perfect square.
841
A square board has an area of 144 square units. How long is each side of the board?
Using prime factorisation, find which of the following are perfect squares.
484
Is 176 a perfect square? If not, find the smallest number by which it should be multiplied to get a perfect square.
