Simplify √300 .(1 point)
Responses
√300 can be simplified as 10√3
To simplify √300, we can first determine if 300 has any perfect square factors. Since 300 is divisible by 100 (which is a perfect square), we can rewrite it as 300 = 100 * 3.
To simplify √300 further, we can now split the square root into two separate square roots:
√300 = √(100 * 3)
Next, we can apply the property of square roots that says the square root of a product is equal to the product of the square roots of each factor. Using this property, we can rewrite the expression as:
√300 = √100 * √3
The square root of 100 is 10, so we have:
√300 = 10√3
Therefore, the simplified form of √300 is 10√3.
To simplify the square root of 300, you can first break down 300 into its prime factors: 300 = 2^2 * 3 * 5^2.
Next, you can simplify the square root expression by taking out the perfect square factors from under the square root: √300 = √(2^2 * 3 * 5^2).
Simplifying further, you can take out the perfect square factors outside the square root: √300 = (2 * 5) * √3.
Finally, multiplying the perfect square factors gives: √300 = 10√3.
Therefore, the simplified form of the square root of 300 is 10√3.