Simplify √300.(1 point)
Responses
10√3
10 start root 3 end root
This radical expression is already fully simplified.
This radical expression is already fully simplified.
5√12
5 start root 12 end root
100√3
100√3
To simplify √300, we can first factorize 300 as the product of its prime factors: 2 x 2 x 3 x 5 x 5.
Next, we can simplify each factor under the square root separately. The square root of 2 x 2 simplifies to 2, and the square root of 3 simplifies to √3. The square root of 5 x 5 simplifies to 5.
Combining these simplified factors, we have 2 x 5 x √3, which can also be written as 10√3.
So, the simplified form of √300 is 10√3.
To simplify the expression √300, you can factor 300 into its prime factors.
First, find the prime factors of 300:
300 = 2 * 2 * 3 * 5 * 5
Next, group the prime factors in pairs and take out any pairs of the same factors from under the square root symbol:
√(2 * 2) * √(3) * √(5 * 5)
Simplifying further, we have:
2 * 2 * √(3) * 5
This simplifies to:
4√3
So the simplified expression is 4√3.