Simplify simplify square root of 300 that be 100 root of three or this radical expression is already fully simplified or five square root of 12 or 10 square root of three

Answer 1

Let's simplify the expressions one by one.

1. Square root of 300: \[ \sqrt{300} = \sqrt{100 \times 3} = \sqrt{100} \times \sqrt{3} = 10\sqrt{3} \] So, \(\sqrt{300} = 10\sqrt{3}\) is the fully simplified form. Therefore, the claim that \(\sqrt{300} = 100\sqrt{3}\) is incorrect.

2. Five times the square root of 12: \[ 5\sqrt{12} = 5\sqrt{4 \times 3} = 5\sqrt{4} \times \sqrt{3} = 5 \times 2\sqrt{3} = 10\sqrt{3} \] So, \(5\sqrt{12} = 10\sqrt{3}\) as well.

To summarize:

• \(\sqrt{300} = 10\sqrt{3}\) is correct.
• \(5\sqrt{12} = 10\sqrt{3}\) is also correct.

You have correctly identified that \(10\sqrt{3}\) is the simplified form of both radical expressions.