Final answer:
To find the length of side x in simplest radical form, we simplify the given square roots. Options 2 and 3 can be simplified to 3√2 and 2√5, while option 4 simplifies to the non-radical number 5.
Step-by-step explanation:
To find the length of side x in simplest radical form with a rational denominator, we must evaluate each of the given options. A radical expression in simplest form means that there are no perfect square factors other than 1 in the radicand, and no fractions in the radicand or denominator when expressed in its simplest form.
Option 1: x = √15
√15 cannot be simplified further because 15 is not divisible by any perfect square other than 1.
Option 2: x = √18
√18 can be simplified because 18 is divisible by 9, which is a perfect square. Hence, √18 = √(9⋅ 2) = √9 ⋅ √2 = 3√2.
Option 3: x = √20
√20 can be simplified because 20 is divisible by 4, which is a perfect square. Thus, √20 = √(4⋅ 5) = √4 ⋅ √5 = 2√5.
Option 4: x = √25
√25 can be simplified to 5 because 25 is a perfect square itself, √25 = 5.
Among the options provided, x = √25 is the only one that simplifies to a non-radical number. Therefore, if the question is seeking the solution in simplest radical form with a rational denominator, options 2 and 3 are valid, which simplify to 3√2 and 2√5 respectively. However, option 4, x = 5, is the simplest non-radical form.