Between the square root of 201, which two consecutive integers does the square root lie

Between the square root of 201, which two consecutive integers does the square root lie? 2. Between the square root of 312, which two consecutive integers does the square root lie? 3. Between the square root of 201, which two consecutive integers does the square root lie? 4. Between the square root of 301, which two consecutive integers does the square root lie? 5. Between the square root of 227, which two consecutive integers does the square root lie? 6. Between the square root of 408, which two consecutive integers does the square root lie? 7. Between the square root of 237, which two consecutive integers does the square root lie? 8. Between the square root of 123, which two consecutive integers does the square root lie? Help

The Correct Answer and Explanation is:

Let’s solve each of the square root problems step by step. We’re trying to find two consecutive integers between which the square root of the given numbers lies.

1. Square Root of 201:

To estimate 201\sqrt{201}201​, we check the perfect squares near 201:

• 142=19614^2 = 196142=196
• 152=22515^2 = 225152=225

Since 196<201<225196 < 201 < 225196<201<225, the square root of 201 lies between 14 and 15.

2. Square Root of 312:

We check the perfect squares near 312:

• 172=28917^2 = 289172=289
• 182=32418^2 = 324182=324

Since 289<312<324289 < 312 < 324289<312<324, the square root of 312 lies between 17 and 18.

3. Square Root of 201 (Repetition):

As we solved this earlier, 201\sqrt{201}201​ lies between 14 and 15.

4. Square Root of 301:

We check the perfect squares near 301:

• 172=28917^2 = 289172=289
• 182=32418^2 = 324182=324

Since 289<301<324289 < 301 < 324289<301<324, the square root of 301 lies between 17 and 18.

5. Square Root of 227:

We check the perfect squares near 227:

• 152=22515^2 = 225152=225
• 162=25616^2 = 256162=256

Since 225<227<256225 < 227 < 256225<227<256, the square root of 227 lies between 15 and 16.

6. Square Root of 408:

We check the perfect squares near 408:

• 202=40020^2 = 400202=400
• 212=44121^2 = 441212=441

Since 400<408<441400 < 408 < 441400<408<441, the square root of 408 lies between 20 and 21.

7. Square Root of 237:

We check the perfect squares near 237:

• 152=22515^2 = 225152=225
• 162=25616^2 = 256162=256

Since 225<237<256225 < 237 < 256225<237<256, the square root of 237 lies between 15 and 16.

8. Square Root of 123:

We check the perfect squares near 123:

• 112=12111^2 = 121112=121
• 122=14412^2 = 144122=144

Since 121<123<144121 < 123 < 144121<123<144, the square root of 123 lies between 11 and 12.

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Summary:

1. 201\sqrt{201}201​ lies between 14 and 15.
2. 312\sqrt{312}312​ lies between 17 and 18.
3. 201\sqrt{201}201​ lies between 14 and 15.
4. 301\sqrt{301}301​ lies between 17 and 18.
5. 227\sqrt{227}227​ lies between 15 and 16.
6. 408\sqrt{408}408​ lies between 20 and 21.
7. 237\sqrt{237}237​ lies between 15 and 16.
8. 123\sqrt{123}123​ lies between 11 and 12.

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This method works because we are finding the closest perfect squares above and below the given number, and using these to estimate the range of the square root.