Simplify √300
√300 can be simplified by finding the prime factors of 300.
The prime factors of 300 are:
2, 2, 3, 5, 5
To simplify the square root of 300, group the prime factors into pairs:
√(2 * 2 * 3 * 5 * 5)
√(2 * 2) * √(3 * 5 * 5)
2 * √(3 * 5 * 5)
2 * √(3 * 25)
2 * √(75)
Now, look for perfect squares within the square root:
2 * √(25 * 3)
2 * 5 * √3
10√3
Therefore, √300 simplifies to 10√3.
To simplify √300, we can determine the square root of its factors.
First, let's find the prime factorization of 300:
300 = 2 × 2 × 3 × 5 × 5.
Next, let's group the factors in pairs of the same number:
300 = (2 × 2) × (3) × (5 × 5).
Now, we can simplify the square root:
√300 = √(2 × 2) × √(3) × √(5 × 5).
Since the square root of a product is equal to the product of the square roots, we can rewrite the expression as:
√300 = 2 × √3 × 5.
Finally, simplifying further, we have:
√300 = 2√3 × 5.
Therefore, the simplified square root of 300 is 2√3 × 5, or 10√3.
To simplify √300, we need to find the largest perfect square that is a factor of 300. In this case, the largest perfect square that divides 300 is 100.
We can rewrite 300 as 100 * 3.
Now, we can simplify the square root of 300 as the square root of 100 times the square root of 3.
The square root of 100 is 10, and the square root of 3 remains as √3.
Therefore, √300 simplifies to 10√3.