Questions: Combine. 6 sqrt(80)-sqrt(5) 6 sqrt(80)-sqrt(5)= (Simplify your answer. Type an exact answer, using radicals as needed.)

Solution Steps

To simplify the expression \(6 \sqrt{80} - \sqrt{5}\), we first simplify the square root of 80. We can express 80 as a product of a perfect square and another number, specifically \(80 = 16 \times 5\). This allows us to simplify \(\sqrt{80}\) to \(4\sqrt{5}\). Then, substitute this back into the expression and combine like terms.

We start with the expression \( 6 \sqrt{80} - \sqrt{5} \). First, we simplify \( \sqrt{80} \): \[ \sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \cdot \sqrt{5} = 4\sqrt{5} \]

Next, we substitute \( \sqrt{80} \) back into the expression: \[ 6 \sqrt{80} = 6 \cdot 4\sqrt{5} = 24\sqrt{5} \] Thus, the expression becomes: \[ 24\sqrt{5} - \sqrt{5} \] Now, we combine like terms: \[ 24\sqrt{5} - 1\sqrt{5} = (24 - 1)\sqrt{5} = 23\sqrt{5} \]

Final Answer