Find the smallest number by which 735 must be multiplied so that the product becomes a perfect square
Answers
Answer:
15 is the smallest number by which 735 must be multiplied.
Step-by-step explanation:
735*15=11025
√11025=105
Answer:
The smallest number by which 735 must be multiplied so the product becomes a perfect square = 15
Step-by-step explanation:
Given number is 735
To find,
The smallest number to be multiplied by 735 so that the product becomes a perfect square.
Solution:
The prime factorization of 735 = 3×5×7²
The smallest number to be multiplied with 735 to get a perfect square = The smallest number to be multiplied with 3×5×7² to get a perfect square
To make the 3×5×7² a perfect square, we need to make each prime factor a perfect square
Since7² is already a perfect square, we need to make 3 and 5 a perfect square
Hence we should multiply 3×5 by 3×5×7² to get a perfect square.
After multiplying, the perfect square we get is 3²×5²×7² = ( 3×5×7)²
∴The smallest number by which 735 must be multiplied so the product becomes a perfect square = 15
#SPJ2