What is 9 square root of 40 simplified?

To simplify \( 9\sqrt{40} \), let's follow these steps:

Step 1: Factorize the number inside the square root.
The number 40 can be factored into \( 4 \times 10 \), where 4 is a perfect square.
So, \( \sqrt{40} = \sqrt{4 \times 10} \).

Step 2: Use the property of square roots.
The square root of a product can be split into the product of square roots:
\( \sqrt{40} = \sqrt{4} \times \sqrt{10} \).

Step 3: Simplify the square root of the perfect square.
\( \sqrt{4} = 2 \). Therefore,
\( \sqrt{40} = 2\sqrt{10} \).

Step 4: Multiply by the coefficient outside the square root.
Since we started with \( 9\sqrt{40} \), substitute \( \sqrt{40} = 2\sqrt{10} \):
\( 9\sqrt{40} = 9 \times 2\sqrt{10} \).

Step 5: Simplify the expression.
\( 9 \times 2 = 18 \), so:
\( 9\sqrt{40} = 18\sqrt{10} \).

Final Answer: \( 9\sqrt{40} \) simplifies to \( 18\sqrt{10} \).