Question
1. list of the first 12 perfect squares
2. True or False: Lynn said that all square roots are irrational numbers. Explain your answer.
3. Classify the numbers as rational or irrational: square root of 77, square root of 48, 0.375654535…., and 0.3757575….
4. find the square root for each number: square root of 121, and square root of 79 - estimate.
5. find the cube roots for each number: cube root of 27^3, and cube root of 75^3 - estimate.
2. True or False: Lynn said that all square roots are irrational numbers. Explain your answer.
3. Classify the numbers as rational or irrational: square root of 77, square root of 48, 0.375654535…., and 0.3757575….
4. find the square root for each number: square root of 121, and square root of 79 - estimate.
5. find the cube roots for each number: cube root of 27^3, and cube root of 75^3 - estimate.
Answers
GPT 3.5
1. The first 12 perfect squares are:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.
2. False. Lynn's statement is incorrect. While some square roots are irrational numbers (such as the square root of 2 or the square root of 3), not all square roots are irrational. For example, the square root of 4 is a rational number (which is 2) since it can be expressed as a fraction.
3. - The square root of 77 is an irrational number.
- The square root of 48 is an irrational number.
- 0.375654535… is an irrational number.
- 0.3757575… is a rational number.
4. - The square root of 121 is 11.
- The square root of 79 is an estimate since it is an irrational number. The estimate could be around 8.8.
5. - The cube root of 27^3 is 27.
- The cube root of 75^3 is an estimate since it is an irrational number. The estimate could be around 43.5.
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144.
2. False. Lynn's statement is incorrect. While some square roots are irrational numbers (such as the square root of 2 or the square root of 3), not all square roots are irrational. For example, the square root of 4 is a rational number (which is 2) since it can be expressed as a fraction.
3. - The square root of 77 is an irrational number.
- The square root of 48 is an irrational number.
- 0.375654535… is an irrational number.
- 0.3757575… is a rational number.
4. - The square root of 121 is 11.
- The square root of 79 is an estimate since it is an irrational number. The estimate could be around 8.8.
5. - The cube root of 27^3 is 27.
- The cube root of 75^3 is an estimate since it is an irrational number. The estimate could be around 43.5.