To find the length of side $AB$ in a right triangle, where $AC$ and $BC$ are the legs, we can apply the Pythagorean Theorem:

$AB^2 = AC^2 + BC^2$

Given:

• $AC = 6$
• $BC = 4$

Substitute these values into the equation:

$AB^2 = 6^2 + 4^2$ $AB^2 = 36 + 16$ $AB^2 = 52$

Now, solve for $AB$:

$AB = \sqrt{52}$ $AB = \sqrt{4 \times 13}$ $AB = 2\sqrt{13}$

So, the length of $AB$ is $2\sqrt{13}$ (approximately 7.21 units).

Would you like further clarification on this or additional details?

Here are 5 related questions for you:

1. What is the Pythagorean Theorem, and why does it apply to right triangles?
2. How can we simplify square roots like $\sqrt{52}$?
3. Can the Pythagorean Theorem be applied to non-right triangles?
4. How would the formula change if we were asked to find the length of one of the legs instead of the hypotenuse?
5. What are some real-world applications of the Pythagorean Theorem?

Tip: Always simplify square roots as much as possible to present the answer in its simplest form.