Final Answer:
8√5 + √20 - √125 = 3√5
Explanation:
In this question, we need to simplify the expression 8√5 + √20 - √125. To simplify the expression, we need to combine like terms. Firstly, the expression has three terms 8√5, √20 and √125. Now, the base of all the three terms is the same, which is √5. Thus, these three terms can be treated as like terms.
Now, we need to add 8√5 and √20. To do that, we need to multiply 8 with √5 to make it as like terms. Thus, we get 8√5 × √5 = 8 × 5 = 40. Thus, 8√5 + √20 = 40 + √20 = 40 + 5 = 45. Thus, the expression reduces to 45 - √125.
Now, we need to subtract √125 from 45. To do that, we need to multiply √125 with √5 to make it as like terms. Thus, we get √125 × √5 = 5 × 5 = 25. Thus, 45 - √125 = 45 - 25 = 20. Thus, the expression reduces to 20/√5.
Finally, we need to divide 20 by √5. To do that, we need to divide 20 by 5 and then take √5 as the denominator. Thus, we get 20/5 = 4. Thus, the answer is 4√5.
Thus, the simplified expression is 8√5 + √20 - √125 = 3√5.