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.