Product of two consecutive natural numbers is 56. Which of the given options can be understood from the given statement?

To determine which options can be derived from the statement that the product of two consecutive natural numbers is 56, we can follow these steps:

1. ### Break Down the Problem

We need to find two consecutive natural numbers $n$ and $n+1$ such that: $n(n + 1) = 56$

2. ### Relevant Concepts

This involves the principles of quadratic equations. We can rewrite the equation as: $n^2 + n - 56 = 0$

3. ### Analysis and Detail

To solve the quadratic equation, we can use the quadratic formula: $n = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ where $a = 1$, $b = 1$, and $c = -56$.

Calculating the discriminant: $b^2 - 4ac = 1^2 - 4(1)(-56) = 1 + 224 = 225$

Now, substituting into the quadratic formula: $n = \frac{-1 \pm \sqrt{225}}{2 \cdot 1} = \frac{-1 \pm 15}{2}$ This gives us two potential solutions:

1. $n = \frac{14}{2} = 7$
2. $n = \frac{-16}{2} = -8$ (not a natural number)

Thus, the valid consecutive natural numbers are $7$ and $8$.

4. ### Verify and Summarize

Verifying the product: $7 \times 8 = 56$ This confirms that the solution is correct.

Final Answer

The two consecutive natural numbers are 7 and 8.