To simplify the radical $\sqrt{150}$, we need to factorize 150 into its prime factors and look for any perfect squares.

1. Start by finding the prime factors of 150: $150 = 2 \times 3 \times 5 \times 5$

2. Next, group the factors to identify perfect squares: $\sqrt{150} = \sqrt{2 \times 3 \times 5 \times 5}$ Notice that $5 \times 5 = 25$ is a perfect square.

3. Extract the square root of 25: $\sqrt{150} = \sqrt{25 \times 6} = \sqrt{25} \times \sqrt{6} = 5\sqrt{6}$

So, the simplified form of $\sqrt{150}$ is $5\sqrt{6}$.

Would you like more details or have any questions?

Here are some related questions:

1. How do you simplify radicals with higher powers?
2. What are the properties of square roots in algebra?
3. How do you simplify expressions involving multiple square roots?
4. How can you estimate the value of non-perfect square roots like $\sqrt{6}$?
5. What are the differences between simplifying square roots and cube roots?

Tip: When simplifying radicals, always look for the largest perfect square factor to extract and simplify the expression efficiently.