Questions: 6 √(32x) - 5 √(18x)

Solution Steps

To simplify the given expression, we need to break down the square roots into their prime factors and then combine like terms.

1. Simplify the square roots by factoring out perfect squares.
2. Combine the simplified terms.

We start with the first term \( 6 \sqrt{32x} \). We can simplify \( \sqrt{32} \) as follows: \[ \sqrt{32} = \sqrt{16 \cdot 2} = 4\sqrt{2} \] Thus, we have: \[ 6 \sqrt{32x} = 6 \cdot 4 \sqrt{2} \sqrt{x} = 24 \sqrt{2} \sqrt{x} \]

Next, we simplify the second term \( -5 \sqrt{18x} \). We can simplify \( \sqrt{18} \) as follows: \[ \sqrt{18} = \sqrt{9 \cdot 2} = 3\sqrt{2} \] Thus, we have: \[ -5 \sqrt{18x} = -5 \cdot 3 \sqrt{2} \sqrt{x} = -15 \sqrt{2} \sqrt{x} \]

Now we combine the simplified terms: \[ 24 \sqrt{2} \sqrt{x} - 15 \sqrt{2} \sqrt{x} = (24 - 15) \sqrt{2} \sqrt{x} = 9 \sqrt{2} \sqrt{x} \]

Final Answer