Evaluate the square root of 84 in radical form.

To evaluate the square root of 84 in radical form, we first need to simplify it. The number 84 can be factored into its prime components.

Prime Factorization of 84

We can break down 84 as follows:

• 84 = 2 × 42
• 42 = 2 × 21
• 21 = 3 × 7

Thus, the prime factorization of 84 is:

84 = 2² × 3 × 7

Simplifying the Square Root

Now, we can express the square root of 84 using its prime factors:

√84 = √(2² × 3 × 7)

Using the property of square roots that states √(a × b) = √a × √b, we can simplify:

√84 = √(2²) × √3 × √7

This simplifies further to:

√84 = 2√21

Final Result

The square root of 84 in radical form is:

2√21