Answer  Hint: Here, in the given question, we have been asked to find the smallest number which when multiplied to \[1100\] gives the number which is a perfect square. And further we are asked to find the square root of the number obtained. We will first factorize the given number and the number which will be left out without a pair will be the desired result. Complete step-by-step answer: To find the smallest number by which the given number should be multiplied so that the product becomes a perfect square, we will first factorize the given number.So, the prime factors of \[1100\] is; \[1100 = 2 \times 2 \times 5 \times 5 \times 11\] Or we can rewrite it as; \[1100 = {\left( 2 \right)^2} \times {\left( 5 \right)^2} \times 11\] Clearly, we can see that the only number left out which is not present in the square is \[11\] .Hence, \[11\] is the smallest number which when multiplied to \[1100\] gives the number that is a perfect square.And the number which will be perfect square number is = \[1100 \times 11\] \[ = 12100\] Now, to find the square root of the number obtained \[12100\] we will factorize it, \[12100 = {\left( 2 \right)^2} \times {\left( 5 \right)^2} \times {\left( {11} \right)^2}\] Hence, the square root is = \[2 \times 5 \times 11\] = \[110\]Note: In mathematics, a square number or a perfect square is a number which is square of any integer. In other words, it is the product of any integer number with itself. And hence, the square root of the perfect square number will always be an integer number. It further means we don’t get the square root of a perfect square in decimal form. |
What is the smallest number that will multiply 12 to make it a perfect square?
Related Posts
Copyright © 2024 SignalDuo Inc.
