This problem involves a right triangle where the lengths of the two legs are $3$ and $5$, and we are solving for the hypotenuse $x$.

We can use the Pythagorean Theorem:

$a^2 + b^2 = c^2$

Here, $a = 3$, $b = 5$, and $c = x$. Substituting the values:

$3^2 + 5^2 = x^2$

$9 + 25 = x^2$

$x^2 = 34$

Taking the square root of both sides:

$x = \sqrt{34}$

Approximating this value:

$x \approx 5.83$

Thus, the hypotenuse $x$ is approximately $\sqrt{34}$, or $5.83$.

Let me know if you'd like further details or clarifications. 😊

Related Questions:

1. What is the Pythagorean Theorem, and where can it be applied?
2. How can you determine if a triangle is a right triangle using side lengths?
3. What are some real-life applications of the Pythagorean Theorem?
4. How do you approximate square roots without a calculator?
5. How can trigonometric functions be used to solve right triangles?

Tip:

Always double-check the units of your answer and ensure the values you use match the question’s requirements!