find the smallest number by which 1100 must be multiplied so that the product becomes a perfect square.Also,find the square root of the perfect square so obtained.
Answers
Answered by
43
The smallest number is 11 by which 1100 must be multiplied and square root of the number is 110.
We have to find the smallest number by which 1100 must be multiplied so that the product becomes a perfect square.
Also, we have to find the square root of the perfect square so obtained.
At first, find prime factor of 1100, this will help to understand which number is needed to multiple to make it a perfect square.
prime factor of 1100 = 1 × 2 × 2 × 5 × 5 × 11
= 2² × 5² × 11¹
you see, The power of 2 and 5 is 2 but the power of 11 is 1 , if we multiply this number with 11, the power of 11 will be 2 after that it becomes a perfect square number.
Therefore the smallest number is 11 by which 1100 must be multiplied so that the product becomes a perfect square.
now new number is 11 × 1100 = 12100
square root of 12100 = √(12100)
= √(2² × 5² × 11²)
= 2 × 5 × 11
= 110
Therefore the square root of the number is 110.
Answered by
2
Answer:
110 is the answer mate
Similar questions