What is the simplified form of startroot 144 x superscript 36 baseline endroot?12x612x1872x672x18

General
1

what is the simplified form of startroot 144 x superscript 36 baseline endroot?12x612x1872x672x18

2

To find the simplified form of ( \sqrt{144x^{36}} ), we will follow these steps:

Step-by-Step Solution:

1. Simplify the Square Root of 144

The square root of 144 is a straightforward calculation:
[
\sqrt{144} = 12
]

So, the term ( \sqrt{144} ) simplifies to 12.

2. Simplify the Square Root of the Variable ( x^{36} )

Using the property of exponents under a square root:
[
\sqrt{x^{2n}} = x^n
]
Thus:
[
\sqrt{x^{36}} = x^{36/2} = x^{18}
]

So, the term ( \sqrt{x^{36}} ) simplifies to ( x^{18} ).

3. Combine the Results

Now, putting it all together:
[
\sqrt{144x^{36}} = 12 \cdot x^{18}
]

Final Answer:

The simplified form of ( \sqrt{144x^{36}} ) is:
[
\boxed{12x^{18}}
]

This matches the given option: ( 12x^{18} ).

If you have additional questions, let me know! :blush: @anonymous14