Question
can you simplify the radical expression sqrt(128w^2)
Answers
GPT 3.5
sqrt(128w^2) = sqrt(64 * 2 * w^2)
= sqrt(64) * sqrt(2) * sqrt(w^2)
= 8w * sqrt(2)
= sqrt(64) * sqrt(2) * sqrt(w^2)
= 8w * sqrt(2)
can you explain in steps?
GPT 3.5
Sure!
1. Break down 128 into its factors: 128 = 64 * 2.
2. Break down w^2 into w * w.
3. Rewrite the expression as sqrt(64 * 2 * w^2).
4. Use the product property of square roots to split the expression into sqrt(64) * sqrt(2) * sqrt(w^2).
5. Simplify sqrt(64) to 8.
6. Simplify sqrt(w^2) to w.
7. Combine the simplifications to get 8w * sqrt(2).
So, sqrt(128w^2) simplifies to 8w * sqrt(2).
1. Break down 128 into its factors: 128 = 64 * 2.
2. Break down w^2 into w * w.
3. Rewrite the expression as sqrt(64 * 2 * w^2).
4. Use the product property of square roots to split the expression into sqrt(64) * sqrt(2) * sqrt(w^2).
5. Simplify sqrt(64) to 8.
6. Simplify sqrt(w^2) to w.
7. Combine the simplifications to get 8w * sqrt(2).
So, sqrt(128w^2) simplifies to 8w * sqrt(2).
can you write it in just the numbers
GPT 3.5
sqrt(128w^2) = sqrt(64 * 2 * w^2)
= sqrt(64) * sqrt(2) * sqrt(w^2)
= 8w * sqrt(2)
= sqrt(64) * sqrt(2) * sqrt(w^2)
= 8w * sqrt(2)