Find the square root of 225−−−√ .(1 point)
The square root of 225 is 15.
To find the square root of 225, follow these steps:
1. Start with the number whose square root you want to find, which is 225 in this case.
2. Begin by estimating the square root. Since 15*15 = 225, you can estimate that the square root of 225 is around 15.
3. Use a method, such as the Babylonian method or long division, to refine your estimate.
If you want to use the Babylonian method, here's how it works:
4. Divide the number you want to find the square root of (225) by your estimate (15). The result is 15.
5. Average the previous result (15) with your estimate (15) to get a new estimate: (15 + 15)/2 = 15.
6. Repeat steps 4 and 5 until you reach the desired level of accuracy or until the estimate doesn't change significantly.
Let's calculate a few iterations of the Babylonian method:
Iteration 1:
Dividing 225 by the initial estimate (15) gives us 15.
The average of 15 and 15 is 15.
The new estimate is 15.
Iteration 2:
Dividing 225 by the new estimate (15) gives us 15.
The average of 15 and 15 is 15.
The new estimate is 15.
Since the estimate didn't change after the second iteration, we can conclude that the square root of 225 is indeed 15.
Therefore, the square root of 225 is 15.
To find the square root of 225, we can use the following steps:
Step 1: Start with the number 225.
Step 2: Divide 225 by any perfect square that we know is a factor of it, such as 25.
225 ÷ 25 = 9
Step 3: Write down the quotient obtained from the previous step.
9
Step 4: Take the average of the quotient obtained and the divisor used in step 2.
(9 + 25) / 2 = 34 / 2 = 17
Step 5: Repeat steps 2, 3, and 4, using the result from step 4 as the new divisor.
225 ÷ 17 = 13.235294...
Step 6: Repeat steps 4 and 5 until you reach desired accuracy.
Following these steps, we find that the square root of 225 is approximately 15.