Question

Select all that are like radicals after simplifying.

a. √50x²
b. √32x
c. √18n
d. √72x²

Answer 1

To determine which expressions are like radicals, we need to simplify each square root expression and check for any common terms. Options a, b, and d are like radicals.

Step-by-step explanation:

To determine which expressions are like radicals, we need to simplify each square root expression. Let's simplify each option:

1. a. √50x²: This expression can be simplified as √(25 * 2 * x²). Taking the square root of 25 gives us 5, so we can rewrite the expression as 5x √2.
2. b. √32x: This expression can be simplified as √(16 * 2 * x). Taking the square root of 16 gives us 4, so we can rewrite the expression as 4x √2.
3. c. √18n: This expression is already simplified, so it remains as √18n.
4. d. √72x²: This expression can be simplified as √(36 * 2 * x²). Taking the square root of 36 gives us 6, so we can rewrite the expression as 6x √2.

After simplifying each expression, we can see that options a, b, and d are like radicals since they all have a √2 term. So the correct options are a, b, and d.