Approximating and Comparing Rational and Irrationals

Front

What is the approximate value of \( \sqrt{8} \)?

Back

Approximately 2.83.

Front

Between which two whole numbers does \( \sqrt{5} \) lie?

Back

Between 2 and 3.

Front

What is an irrational number?

Back

An irrational number is a non-repeating, non-terminating decimal.

Front

What is the approximate value of \( \sqrt{11} \)?

Back

Approximately 3.32.

Front

Which number is closer to \( \sqrt{8} \), 2.5 or 3?

Back

3 is closer to \( \sqrt{8} \) (approximately 2.83).

Front

What is the difference between rational and irrational numbers?

Back

Rational numbers can be expressed as a fraction of two integers, while irrational numbers cannot.

Front

What is the decimal representation of \( \sqrt{2} \)?

Back

Approximately 1.41.

Front

How can you approximate the value of a square root?

Back

By finding two perfect squares it lies between and estimating.

Front

What is the value of \( \sqrt{9} \)?

Back

3.

Front

What is the significance of non-repeating decimals in identifying irrational numbers?

Back

Non-repeating decimals indicate that the number cannot be expressed as a fraction.