√(999^2)=√(999) × √???
√(a^2) = (√a)(√a) = a
I figured the formula out but still thanks
To find the value of √(999^2), we can start by simplifying 999^2.
999^2 means 999 multiplied by itself, so 999^2 = 999 * 999.
To simplify this multiplication, we can break down 999 into its prime factors, which are 3 and 37.
999 = 3 * 37.
So, 999^2 = (3 * 37)^2 = 3^2 * 37^2 = 9 * 1369.
Now, let's calculate the square root of 9 * 1369.
√(9 * 1369) = √(9) * √(1369).
Since the square root of 9 is 3, we have:
3 * √(1369).
To simplify further, we need to find the square root of 1369.
The square root of 1369 is a whole number, which is 37.
So, √(999^2) = 3 * √(1369) = 3 * 37 = 111.
Therefore, √(999^2) = 111.
To summarize the process:
1. Calculate 999^2 = 999 * 999.
2. Break down 999 into its prime factors: 999 = 3 * 37.
3. Substitute the prime factors into the multiplication: 999^2 = (3 * 37)^2 = 3^2 * 37^2 = 9 * 1369.
4. Simplify the square root: √(9 * 1369) = √(9) * √(1369) = 3 * √(1369).
5. Calculate the square root of 1369, which is 37.
6. Multiply the result by 3 to get the final answer: 3 * 37 = 111.