How many non perfect square numbers are there between 289 and 324?

To find the number of non-perfect square numbers between 289 and 324, we first identify the perfect squares within this range.

Identifying Perfect Squares

The perfect squares between 289 and 324 are:

• 289 (which is 17²)
• 300 (not a perfect square)
• 301 (not a perfect square)
• 302 (not a perfect square)
• 303 (not a perfect square)
• 304 (not a perfect square)
• 305 (not a perfect square)
• 306 (not a perfect square)
• 307 (not a perfect square)
• 308 (not a perfect square)
• 309 (not a perfect square)
• 310 (not a perfect square)
• 311 (not a perfect square)
• 312 (not a perfect square)
• 313 (not a perfect square)
• 314 (not a perfect square)
• 315 (not a perfect square)
• 316 (not a perfect square)
• 317 (not a perfect square)
• 318 (not a perfect square)
• 319 (not a perfect square)
• 320 (not a perfect square)
• 321 (not a perfect square)
• 322 (not a perfect square)
• 323 (not a perfect square)
• 324 (which is 18²)

Counting Non-Perfect Squares

Now, we can see that the perfect squares in this range are 289 and 324. The numbers between them are:

• 290
• 291
• 292
• 293
• 294
• 295
• 296
• 297
• 298
• 299
• 300
• 301
• 302
• 303
• 304
• 305
• 306
• 307
• 308
• 309
• 310
• 311
• 312
• 313
• 314
• 315
• 316
• 317
• 318
• 319
• 320
• 321
• 322
• 323

Counting these numbers gives us a total of 33 numbers. Since only 2 of them (289 and 324) are perfect squares, we subtract these from the total:

Final Calculation

Thus, the number of non-perfect square numbers between 289 and 324 is:

33 - 2 = 31

In summary, there are 31 non-perfect square numbers between 289 and 324.