Problem 263

Solution 1

We rewrite the left side of the given equation as $5 \times 6 \times (2 \times 3) \times (2 \times 3)$.

Since $5 \times 6 \times (2 \times 3) \times (2 \times 3) = 5 \times 6 \times n \times n$, then a possible value of $n$ is $2 \times 3$ or 6.

Solution 2

Since $2 \times 2 \times 3 \times 3 \times 5 \times 6 = 5 \times 6 \times n \times n$, then $1080 = 30n^2$ or $n^2 = 36$.

Thus, a possible value of $n$ is 6. (The second possible value for $n$ is $-6$.)

Solution 3

Dividing both sides by $5 \times 6$, we obtain $2 \times 2 \times 3 \times 3 = n \times n$, which is equivalent to $n^2 = 36$.

Thus, a possible value of $n$ is 6. (The second possible value for $n$ is $-6$.)