To simplify the square root of 63, let's break it down:

1. Find the prime factorization of 63.

   • 63 = 9 × 7
   • 9 can be written as 3², so:
     63 = 3² × 7

2. The square root of 63 becomes: $\sqrt{63} = \sqrt{3² \times 7}$

3. Use the property of square roots:
   $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ So, $\sqrt{63} = \sqrt{3²} \times \sqrt{7} = 3\sqrt{7}$

Therefore, the simplified form of the square root of 63 is 3√7.

Would you like further explanation or details on how this works?

Here are five related questions:

1. How do you simplify square roots of other numbers like 48 or 72?
2. What is the difference between rational and irrational square roots?
3. Can square roots of non-perfect squares ever be simplified fully?
4. What is the process of simplifying cube roots or higher roots?
5. How do you approximate square roots when simplification isn't possible?

Tip: When simplifying square roots, always start by factoring the number into primes and look for perfect square factors.