1. **State the problem:** Simplify the division problem $5\sqrt{45}$, which means divide 45 by 5 using long division. 2. **Recall the division formula:** Division is splitting a number (dividend) into equal parts defined by the divisor. The quotient is the result. 3. **Perform the division:** $$\frac{45}{5}$$ 4. **Simplify step-by-step:** - Divide 45 by 5. - Since $5 \times 9 = 45$, the quotient is 9. 5. **Final answer:** $$5\sqrt{45} = 9$$ This means 45 divided by 5 equals 9. This process applies similarly to other division problems like $4\sqrt{88}$, $6\sqrt{96}$, etc., but here we only solve the first as per instructions.