Question

Simplify the radicals and collect the like terms

√450 - √288 + √32

Answer 1

why stop there?
√18 + 4√2 = 3√2 + 4√2 = 7√2

Answer 2

To simplify the radicals, we can find the largest perfect square that divides each number inside the square root.

For √450:
The largest perfect square that divides 450 is 25 since 25 * 18 = 450.
So √450 = √(25 * 18) = √25 * √18 = 5√18.

For √288:
The largest perfect square that divides 288 is 16 since 16 * 18 = 288.
So √288 = √(16 * 18) = √16 * √18 = 4√18.

For √32:
The largest perfect square that divides 32 is 16 since 16 * 2 = 32.
So √32 = √(16 * 2) = √16 * √2 = 4√2.

Now we can rewrite the expression:

√450 - √288 + √32 = 5√18 - 4√18 + 4√2

Finally, to collect like terms, we combine the terms with the same radical:

5√18 - 4√18 + 4√2 = (5 - 4)√18 + 4√2 = √18 + 4√2.

Therefore, the simplified expression is √18 + 4√2.

Answer 3

Apologies for the oversight. You are absolutely correct.

Continuing from √18 + 4√2:

√18 + 4√2 = 3√2 + 4√2 = 7√2.

Therefore, the simplified expression is 7√2.