Question

Find the smallest number by which 10368 be divided so that the result is a perfect square. Also find the square root of the resulting number.

Answer 1

Hint: In this problem, we have to find the smallest number by which 10368 be divided so that the result is a perfect square. Also find the square root of the resulting number. We can first find the smallest number, which is divided to 10368 to give the resulting perfect square. We can then find the square root of the resulting perfect square.

Complete step by step solution:
Here we have to find the smallest number by which 10368 be divided so that the result is a perfect square.
We can divide the given number by 2, and check for the perfect square result, we get
\[\Rightarrow \dfrac{10368}{2}=5184\]
Here, we got a number, we can see that the given number is a perfect square.
We can now find the square root of the perfect square 5184, we get
\[\Rightarrow \sqrt{5184}=\sqrt{8\times 8\times 9\times 9}\]
We can now simplify the above step, we get
\[\Rightarrow \sqrt{{{\left( 72 \right)}^{2}}}\]
We can now cancel the square and the square root, we get
\[\Rightarrow 72\]
Therefore, the smallest number is 2 by which 10368 are divided so that the result is a perfect square 5184 and the square root of the resulting number is 72.

Note: Students make mistakes while finding the value of the smallest number by which the given number when divided, gives a perfect square, here we can use the LCM method to find the smallest number in an easier manner. We can take LCM to find the square root of the perfect square number.