The value of $\sqrt{150}$ can be simplified as follows:

First, break down 150 into its prime factors: $150 = 2 \times 3 \times 5^2$

Now, apply the square root: $\sqrt{150} = \sqrt{2 \times 3 \times 5^2}$

Since $\sqrt{5^2} = 5$, we can simplify: $\sqrt{150} = 5 \times \sqrt{6}$

Thus, $\sqrt{150}$ simplifies to: $\boxed{5\sqrt{6}}$

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

Here are 5 related questions to explore:

1. What is $\sqrt{200}$ simplified?
2. How can we estimate $\sqrt{6}$ to a decimal value?
3. How do we calculate cube roots like $\sqrt[3]{150}$?
4. What are the properties of square roots of prime numbers?
5. How can $\sqrt{150}$ be used in solving quadratic equations?

Tip: When simplifying square roots, always check for perfect squares in the factorization!