Find the square root of 250.(1 point)
Responses
510−−√
5 start root 10 end root
250
250
105–√
10 start root 5 end root
2510−−√
10√25
To find the square root of 250, you can use a calculator or simplify it manually.
If you use a calculator, the square root of 250 is approximately 15.811.
If you want to simplify it manually, here's the step-by-step process:
Step 1: Start by factoring the number inside the square root, 250.
250 = 25 * 10
Step 2: Take the square root of the perfect square part, which is 25.
√25 = 5
Step 3: Bring down the remaining factor outside the square root, which is 10.
√250 = 5√10
So, the simplified square root of 250 is 5√10.
To find the square root of 250, you can either calculate it manually or use a calculator. Here's how you can find it manually:
1. Start by estimating the square root. One way to estimate is to find the two perfect square numbers that the given number (250) lies between. In this case, 16^2 is 256, and 15^2 is 225. So, 250 falls between these two numbers.
2. Take the average of the two perfect squares as your initial estimate. In this case, the average of 16 and 15 is 15.5. So, you can start with an estimate of 15.5.
3. Divide the given number (250) by your initial estimate (15.5). The result is approximately 16.13.
4. Now, take the average of your initial estimate (15.5) and the result of the division (16.13). The result is 15.815.
5. Repeat steps 3 and 4 until your estimate becomes accurate enough. After a few repetitions, you will find that the square root of 250 is approximately 15.81.
So, the correct response is option: 15.81