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To answer whether the discriminant in your solution is a perfect square, let's break down the steps.

You have the quadratic equation:

\[
x^2 - 8x + 9 = 0
\]

The discriminant, \( \Delta \), for a quadratic equation \( ax^2 + bx + c = 0 \) is calculated as:

\[
\Delta = b^2 - 4ac
\]

Here, \( a = 1 \), \( b = -8 \), and \( c = 9 \), so:

\[
\Delta = (-8)^2 - 4(1)(9) = 64 - 36 = 28
\]

The discriminant is \( 28 \). Now, to determine if 28 is a perfect square:

- The square root of 28 is approximately 5.29, which is not an integer.
- Hence, 28 is **not** a perfect square.

Since the discriminant is not a perfect square, the quadratic equation has two distinct irrational roots.

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Do you have any questions or need further details?  
Here are 5 related questions that might interest you:

1. How do irrational roots differ from rational roots in quadratic equations?
2. What happens if the discriminant equals zero in a quadratic equation?
3. How do you solve a quadratic equation using the quadratic formula?
4. Can a quadratic equation have imaginary roots, and when does that happen?
5. How does the discriminant relate to the graph of a quadratic function?

**Tip:** If the discriminant is a perfect square, the quadratic equation will have rational roots.

Find the nature of roots of the equation x^2 - 8x + 9 = 0.

Learn how to determine the nature of roots of the quadratic equation x^2 - 8x + 9 using the discriminant formula. This problem focuses on calculating the discriminant and interpreting the result to understand the nature of the roots. Suitable for students in Grades 9-10.

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