Question

Write the radical in simplest radical form. decimals not allowed. (4 points – from lesson 5.03). √ 5 12

Answer 1

The simplest radical form of √(5 × 12) is 2√(5)√3, after performing prime factorization on the number 12 and simplifying.

Step-by-step explanation:

We are asked to simplify the radical √(5 × 12) to its simplest form. To do this, we will factor 12 into its prime factors and look for pairs of identical factors, since √x² = x.

The prime factorization of 12 is 2²× 3.

So, we can write √(5 × 12) as √(5 × 2² × 3).

This simplifies to √(5 × 2²) × √3, which further simplifies to 2√(5) × √3.

Since there are no further pairs of identical prime factors, 2√(5)√3 is the simplest radical form.