To solve $\sqrt{7} + \sqrt{63}$, we first simplify the square roots:

Step 1: Simplify $\sqrt{63}$

The number 63 can be factored as: $63 = 9 \times 7$ Since 9 is a perfect square ($\sqrt{9} = 3$), we simplify: $\sqrt{63} = \sqrt{9 \cdot 7} = \sqrt{9} \cdot \sqrt{7} = 3\sqrt{7}.$

Step 2: Combine $\sqrt{7} + 3\sqrt{7}$

Now, the expression becomes: $\sqrt{7} + 3\sqrt{7} = 4\sqrt{7}.$

Final Answer:

$4\sqrt{7}.$

Would you like further explanation or have any questions?

Related Questions:

1. How do you simplify square roots that are not perfect squares?
2. What is the importance of factoring in simplifying radicals?
3. How would you simplify an expression like $2\sqrt{12} + 3\sqrt{27}$?
4. Can you explain how to handle square roots in addition or subtraction problems?
5. How do you convert radical expressions into decimal approximations?

Tip:

Always check for perfect square factors when simplifying square roots, as it makes addition or subtraction easier!