Let's simplify the given expression:

$5\sqrt{12} + \sqrt{48} - \sqrt{8}$

Step 1: Simplify the Square Roots

We break each square root into its prime factors:

1. $\sqrt{12}$
   $\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}$ So, $5\sqrt{12} = 5(2\sqrt{3}) = 10\sqrt{3}$.

2. $\sqrt{48}$
   $\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}$

3. $\sqrt{8}$
   $\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}$

Step 2: Combine Like Terms

$10\sqrt{3} + 4\sqrt{3} - 2\sqrt{2}$

$(10 + 4)\sqrt{3} - 2\sqrt{2}$

$14\sqrt{3} - 2\sqrt{2}$

Since $\sqrt{3}$ and $\sqrt{2}$ are different radicals, we cannot simplify further.

Final Answer:

$\mathbf{14\sqrt{3} - 2\sqrt{2}}$

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Would you like a more detailed breakdown of any step?

Related Questions:

1. How do you simplify $\sqrt{75} + \sqrt{27}$?
2. What is the process for rationalizing a denominator with square roots?
3. How do you simplify expressions with cube roots?
4. What are the properties of square roots that help with simplification?
5. Can you simplify $\sqrt{50} - 2\sqrt{18} + 3\sqrt{8}$?

Tip:

When simplifying square roots, always look for the largest perfect square factor to extract square roots efficiently.