simplfy square root (300) is it 10 square root(3) if so why
Yes, your simplification is correct: √300 can be simplified to 10√3.
To understand why, we need to find the largest perfect square that can be factored out of 300. In this case, it is 100 (since 10² = 100). Therefore, we can write 300 as 100 * 3. Taking the square root, we then get: √300 = √(100 * 3). By the properties of square roots, this can be further simplified as the product of the square root of 100 (which is 10) and the square root of 3, resulting in 10√3.
To simplify the square root of 300, we need to break down 300 into its prime factors.
The prime factorization of 300 is:
300 = 2 * 2 * 3 * 5 * 5
Now, we can rewrite the square root of 300:
√300 = √(2 * 2 * 3 * 5 * 5)
Since square roots can be separated into pairs, we can write it as:
√300 = (√2 * √2 * √3 * √5 * √5)
Simplifying further, we get:
√300 = 2 * √3 * 5
Finally, we can multiply the numbers outside the square root:
√300 = 10√3
So the simplified form of √300 is 10√3.
To simplify the square root of 300, we need to find the largest perfect square that divides evenly into 300. In this case, the largest perfect square is 100, because 100 * 3 = 300.
So, we can rewrite the square root of 300 as the square root of 100 times the square root of 3: √100 * √3.
The square root of 100 is 10, so we can now simplify further: 10 * √3.
Therefore, √300 simplifies to 10√3.
The reason we can simplify it to 10√3 is that √300 is equal to the square root of 100 times the square root of 3. Since the square root of 100 is 10, we can replace it in the expression, giving us 10 * √3, or 10√3.