Simplify √300
1. 100√3
2. 10√3
3. This radical expression is already fully simplified
4. 5√12
To simplify √300, we can break down the number 300 into its factors: 300 = 100 * 3.
Using the property of radicals, we can rewrite √300 as √(100 * 3).
This can be further simplified as follows:
√(100 * 3) = √100 * √3
Since √100 = 10 and √3 is already fully simplified, we can simplify √300 to 10√3.
Therefore, the correct answer is 2. 10√3.
To simplify √300, we can first simplify the square root of 300 by factoring it into its prime factors.
The prime factorization of 300 is:
300 = 2 * 2 * 3 * 5 * 5
Now, we can simplify the square root by taking out matching pairs of prime factors from under the square root sign. Since there are two 2s and two 5s, we can take them outside the square root sign:
√300 = √(2 * 2 * 3 * 5 * 5)
= 2 * 5 * √(3)
= 10√3
So, the simplified form of √300 is 10√3. Therefore, the correct answer is option 2.
To simplify the expression √300, we need to find the largest perfect square that divides evenly into 300.
First, let's prime factorize 300:
300 = 2 * 2 * 3 * 5 * 5
Now, we look for perfect squares in the prime factorization. We have two pairs of "2" and one pair of "5".
Taking one pair of "2" and one pair of "5" gives us 2 * 2 * 5 * 5 = 100, which is a perfect square.
So, we can rewrite 300 as 100 * 3.
The square root of 100 is 10, so we can simplify further:
√300 = √(100 * 3) = √100 * √3 = 10√3
Therefore, the simplified form of √300 is option 2: 10√3.