The answer to the question is 3√7.
How can you solve this problem?
To solve this problem, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the side with length x, and the other two sides have lengths 3 and √6.
Pythagorean Theorem:
x² = 3² + √6²
Solving for x:
x² = 9 + 6
x² = 15
x = √15
Now, we can simplify √15 by factoring it into its prime factorization:
√15 = √(3 x 5)
The square root of 3 cannot be simplified further, but the square root of 5 can be simplified to √5.
√15 = √3 x √5
Therefore, the answer to the question is 3√7.