We are given the number 243, which is not a perfect square. We need to find the smallest natural number that we can multiply 243 by to obtain a perfect square.

1. Problem Description

We are given the number 243, which is not a perfect square. We need to find the smallest natural number that we can multiply 243 by to obtain a perfect square.

2. Solution Steps

First, we find the prime factorization of

2

4

3. $243 = 3 \times 81 = 3 \times 9 \times 9 = 3 \times 3 \times 3 \times 3 \times 3 = 3^5$.

So, $243 = 3^5$.

For a number to be a perfect square, all the exponents in its prime factorization must be even. In the prime factorization $3^5$, the exponent is 5, which is odd. To make it even, we need to multiply $3^5$ by $3^1$.

Then $3^5 \times 3^1 = 3^6 = (3^3)^2 = 27^2 = 729$.

Therefore, $243 \times 3 = 729$, which is a perfect square ($27^2$).

So, the smallest natural number to multiply 243 by to get a perfect square is

3.

3. Final Answer

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