Simplify the radical expression.
√72x^2
A. 36√x^2
B. 6x √2 *****
C. x√36
D. 6√2x^2
looks good
To simplify the radical expression √72x^2, follow these steps:
Step 1: Write 72 as the product of its prime factors.
72 = 2 * 2 * 2 * 3 * 3 = 2^3 * 3^2
Step 2: Simplify the square root of the perfect square term.
√(2^2 * x^2) = 2x
Step 3: Write the remaining term under the square root sign.
√(3^2 * 2) = 3√2
Combining the simplified terms gives us the final answer:
√72x^2 = 2x * 3√2 = 6x√2
Therefore, the simplification of the radical expression √72x^2 is option B. 6x√2.
To simplify the radical expression √72x², start by breaking down the radicand (the number under the square root) into its prime factors:
√(72x²) = √(2² × 2² × 3² × x²)
Since the square root (√) can be separated into two square roots, one for perfect squares and one for non-perfect squares, we can simplify the expression further:
√(2² × 2² × 3² × x²) = (√4 × √4 × √9 × √x²)
Next, simplify the perfect square roots:
(2 × 2 × 3 × x) = 12x
Therefore, the simplified radical expression is 12x, which corresponds to option B.