give a step by step for these problems: Directions:  For  the  following  expressions,  please  simplify  the 

radicals into its  simplest  form.  Please  Show  Your  Work. 

1.  √16 

2.  √32 

Let's go through the process of simplifying each radical step by step.

### 1. Simplifying \(\sqrt{16}\)

**Step 1:** Identify if the number inside the square root is a perfect square.

- \(16\) is a perfect square because it can be written as \(4 \times 4\).

**Step 2:** Take the square root of the perfect square.

\[
\sqrt{16} = 4
\]

**Conclusion:** The simplified form of \(\sqrt{16}\) is \(4\).

---

### 2. Simplifying \(\sqrt{32}\)

**Step 1:** Factor the number inside the square root into its prime factors or into a product that includes a perfect square.

- \(32\) can be factored as \(32 = 16 \times 2\).

**Step 2:** Break down the square root into the square root of each factor.

\[
\sqrt{32} = \sqrt{16 \times 2}
\]

**Step 3:** Simplify the square root of the perfect square.

- Since \(\sqrt{16} = 4\), substitute this into the equation:

\[
\sqrt{32} = 4 \times \sqrt{2}
\]

**Conclusion:** The simplified form of \(\sqrt{32}\) is \(4\sqrt{2}\).

---

These steps can be applied to any square root simplification process. 

Would you like any further details or explanations on this? Here are 5 additional related questions:

1. How do you simplify \(\sqrt{50}\) step by step?
2. What steps would you take to simplify \(\sqrt{72}\)?
3. Can you show the steps for simplifying \(\sqrt{45}\)?
4. What is the step-by-step process for simplifying \(\sqrt{18}\)?
5. How do you simplify a square root that is not a perfect square?

**Tip**: When simplifying radicals, always check if the number inside the radical has a perfect square factor, as this will make the simplification easier.

Learn how to simplify square roots √16 and √32 into their simplest form with detailed step-by-step solutions. These problems involve identifying perfect squares and factoring techniques. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation