Simplify. \( \sqrt{60 a^{3}} \)

To simplify \( \sqrt{60 a^{3}} \), start by breaking it down. The number 60 can be factored into \( 4 \times 15 \) or \( 4 \times 3 \times 5 \). The square root of 4 is 2, so we can take that out of the square root. For \( a^{3} \), we can express it as \( a^{2} \cdot a \), allowing us to take out \( a \). Putting it all together: \[ \sqrt{60 a^{3}} = \sqrt{4 \times 15 \times a^{2} \times a} = \sqrt{4} \cdot \sqrt{15} \cdot \sqrt{a^{2}} \cdot \sqrt{a} = 2a\sqrt{15a} \] Thus, the simplified form is \( 2a\sqrt{15a} \).