Simplify the expression below and leave your expression in exact form with coefficient a and radicand b so we have :  a\sqrt[]{b} 
  \sqrt[]{48}  

To simplify the square root of 48, we start by factoring 48 into its prime factors:

\[
48 = 2 \times 24 = 2 \times 2 \times 12 = 2 \times 2 \times 2 \times 6 = 2 \times 2 \times 2 \times 2 \times 3 = 2^4 \times 3
\]

Next, we use the property of square roots that states:

\[
\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}
\]

So, we can break down the square root:

\[
\sqrt{48} = \sqrt{2^4 \times 3} = \sqrt{2^4} \times \sqrt{3}
\]

Since \(\sqrt{2^4} = 2^2 = 4\), we have:

\[
\sqrt{48} = 4\sqrt{3}
\]

Thus, the simplified form of \(\sqrt{48}\) is:

\[
4\sqrt{3}
\]

Here, \(a = 4\) and \(b = 3\).

Would you like more details on the simplification process or have any other questions?

Here are 5 related questions:
1. How would you simplify \(\sqrt{72}\) using the same method?
2. What is the simplified form of \(\sqrt{75}\)?
3. How do you simplify \(\sqrt{50}\)?
4. How would you express \(\sqrt{12}\) in the form \(a\sqrt{b}\)?
5. What happens if the radicand is a perfect square, like \(\sqrt{49}\)?

**Tip:** Always look for perfect square factors when simplifying square roots; they make the simplification process easier.

Simplify the expression below and leave your expression in exact form with coefficient a and radicand b so we have: a√b √48

Learn how to simplify the square root of 48 in exact form with a detailed step-by-step solution. We break down the radicand using prime factorization and apply the property of square roots. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation