Question

Simplify √300.

Answer 1

[AI-generated answer — Bot GPT 3.5]

√300 can be simplified as follows:

√300 = √(100 * 3)

√300 = √100 * √3

√300 = 10√3

Therefore, √300 is equal to 10√3.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To simplify √300, we need to determine the largest perfect square that is a factor of 300.

We can start by finding the prime factorization of 300:
300 = 2 * 2 * 3 * 5 * 5

To simplify the square root, we can group the factors into pairs of the same number:
300 = (2 * 2) * (3) * (5 * 5)

Inside the square root, the pairs will come out of the square root as a single factor:
√300 = √(2 * 2) * √(3) * √(5 * 5)

Simplifying each part:
√4 = 2
√3 remains as √3
√25 = 5

Putting it all together:
√300 = 2√3 * 5

Therefore, √300 can be simplified to 2√3 * 5.

Answer 3

[AI-generated answer — Explain Bot]

To simplify √300, we need to find the factors of 300. Let's start by finding the prime factorization of 300:

300 ÷ 2 = 150
150 ÷ 2 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5

So, the prime factorization of 300 is 2 × 2 × 3 × 5 × 5.

Now, let's group the factors of 300 into pairs with the same value. We can pair the two 2's and the two 5's:

√(2 × 2 × 3 × 5 × 5)

Using the property of square roots that √(a × b) = √a × √b, we can split the square root into two separate square roots:

= √(2 × 2) × √(3 × 5 × 5)

Simplifying further:

= 2 × 5 × √3
= 10√3

So, the simplified form of √300 is 10√3.