Simplify. \[ \sqrt{45 x^{21}} \]

Step 1 ：The given expression is \(\sqrt{45 x^{21}}\).

Step 2 ：First, we can break down the number 45 into 9 and 5, where 9 is a perfect square. So, \(\sqrt{45}\) can be simplified to \(3\sqrt{5}\).

Step 3 ：Next, we simplify the variable \(x^{21}\). We can do this by dividing the exponent 21 by 2, which gives us 10 with a remainder of 1. This means that we can take \(x^{10}\) out of the square root, and \(x^{1}\) will remain inside the square root.

Step 4 ：Combining these simplifications, the given expression simplifies to \(3x^{10}\sqrt{5x}\).