2. Give an example of a rational number nd an example of an irrational that falls between the values of v8 and v64.
One example of a rational number between the values of √8 and √64 is √16 (which is equal to 4). √16 is rational because it can be expressed as a fraction, 4/1.
One example of an irrational number between the values of √8 and √64 is √15, which is approximately 3.87298. √15 is irrational because it cannot be expressed as a fraction or a terminating or repeating decimal.
2. Give an example of a rational number nd an example of an irrational that falls between the values of v8 and 3v64
One example of a rational number between the values of √8 and 3√64 is √16 (which is equal to 4). √16 is rational because it can be expressed as a fraction, 4/1.
One example of an irrational number between the values of √8 and 3√64 is √15, which is approximately 3.87298. √15 is irrational because it cannot be expressed as a fraction or a terminating or repeating decimal.
Sure! To provide an example of a rational number between √8 and √64, we can take their average.
√8 ≈ 2.8284 and √64 = 8.
So, their average would be (2.8284 + 8)/2 = 5.4142.
Therefore, 5.4142 is a rational number between √8 and √64.
Now, for an example of an irrational number, we can use π (pi) which is approximately 3.14159.
π is an irrational number because it cannot be expressed as a finite decimal or a fraction, and it goes on infinitely without a repeating pattern.
Hence, π is an irrational number that falls between √8 and √64.