Evaluate square root of 289

Problem

√(,289)

Solution

1. Identify the number under the radical, which is 289

2. Determine if 289 is a perfect square by testing integers.

3. Calculate the square of 10 which is 100 and the square of 20 which is 400 Since 100<289<400 the square root must be between 10 and 20

4. Observe the last digit of 289 which is 9 This suggests the square root ends in either 3 or 7 because 3=9 and 7=49

5. Test the integer 17 by multiplying 17×17

6. Verify the multiplication: 17×17=289

Final Answer

√(,289)=17

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