Rational vs. Irrational
Is 2/3 a rational number or an irrational number?
In decimal form, it is a recurring decimal.
Maddy and Jasmine are working on a question: 6.3 -(-1.5), when Jasmine says her answer is a rational number, but Maddy disagrees, saying the answer is irrational. Who's in the wrong in this?
Maddy is the wrong because the decimals used in the equation is finite (meaning the answer is rational).
Explain what classifies a number as rational?
Answer:
-A number that can be written as a fraction.
-A decimal that terminates or repeates.
Solve.
the square root of 6 times the square root of 2
What is: 3.464?
True or False: The square root of 100 is an irrational number.
What is: False?
Numbers that are either integers, whole numbers, or finite numbers are considered rational.
Is the square root of 400 rational or irrational?
What is: Rational?
The square root of 400 is 20 (rational).
Cassidy says that 3.745483 (3 repeated) is irrational, while Allie says that it's rational. Who's wrong?
Allie is wrong because infinite decimals are irrational.
Explain what makes a number irrational.
Answer:
-Cannot be written as a fraction.
-Decimal that does not terminate or repeat.
Solve:
the square root of 6 (the square root of 5)
5.477
Is 2.67676767 rational or irrational?
Rational. Since the .67 is finite, it is considered rational.
Lia says that the square root of 64 is irrational. Her twin sister, Lexi says that its rational. Who is in the wrong?
Lexi is correct because 8 is a rational number.
Explain whether 4.4444... is rational or irrational. Then explain why.
Answer: Rational because it is a repeating decimal
Solve:
square root of 30 times the square root of 5
12.247
True or false: The product of two rational numbers is irrational.
False; two rational numbers = a rational number
Is the square root of 47 rational or irrational?
Irrational.
Jeff and Aaron are working on a worksheet, when Jeff realizes the sum of the square root and 2 and the square root of 5 is rational. However, Aaron says the answer is irrational. Who's wrong?
Jeff is wrong because the decimal seems to be infinite.
Explain whether pi is rational or irrational. Then explain why.
Answer:
-Pi is irrational because it equals 3.14592...
-It is a decimal that does not repeat or terminate.
Solve:
square root of 15 times square root of 2
5.4772...
True or false: the square root of 64 and the square root of 4 is rational.
True.
Is the square root of 28 rational or irrational?
Irrational.
Eleanor and her friend Susana are working on a worksheet, when Susana says that the product of the square root of 16 and the square root of 25 is rational. Eleanor disagrees, saying that its irrational. Who's wrong?
Explain whether 8.116111611116... is rational or irrational. Then explain why.
Answer:
This number is irrational because it does not repeat or terminate.
Solve.
the square root of 20 times the square root of 4
Answer: 8.94427191
True or false? The product of a rational number and a rational number leads to an rational number.
True.