https://file.aiquickdraw.com/mathbot/file/1726764576641l10tsk21.jpg

The image asks to multiply the expression \(\sqrt{14v} \cdot \sqrt{2}\) and simplify it, assuming \(v \geq 0\).

### Solution:

We can use the property of square roots:
\[
\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}
\]

So,
\[
\sqrt{14v} \cdot \sqrt{2} = \sqrt{14v \cdot 2} = \sqrt{28v}
\]

Now, we check if \(\sqrt{28v}\) can be simplified. We break down 28:
\[
28 = 4 \cdot 7
\]
Thus,
\[
\sqrt{28v} = \sqrt{4 \cdot 7v} = \sqrt{4} \cdot \sqrt{7v} = 2\sqrt{7v}
\]

### Final Answer:
\[
2\sqrt{7v}
\]

Would you like any further details or explanations?

Here are 5 related questions to expand your understanding:
1. How do you simplify square roots when the radicand contains variables?
2. Can the product of two square roots always be combined into one root?
3. How would you solve if the variables inside the square root are negative?
4. What are other properties of square roots that can simplify expressions?
5. How do you rationalize a denominator when a square root is involved?

**Tip:** Always factor out perfect squares when simplifying square roots to ensure the simplest form.

Multiply: \(\sqrt{14v} \cdot \sqrt{2}\). Assume v is greater than or equal to zero, and write your answer in simplest form.

Learn how to simplify the expression \(\sqrt{14v} \cdot \sqrt{2}\) step by step. This problem explores key algebraic concepts such as multiplying square roots and simplifying radicals. 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