Rational vs. Irrational
Is 2/3 a rational number or an irrational number? Explain.
Rational because it is already in fraction form.
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? Explain
Maddy is the wrong because the answer is 7.8 which is a terminating decimal, and it is rational.
Find the sum of the following problem:
7/3 - 5/3 = ___
Answer: 2/3 or 0.66...
Solve.
the square root of 6 times the square root of 2
Ans: 3.464...
True or False: The square root of 100 is an irrational number.
Explain
What is: False?
square root of 100 = 10 (whole number/integer) rational number
Is the square root of 400 rational or irrational? Explain
What is: Rational?
The square root of 400 is 20 (rational). 20 is a whole number/integer
Cassidy says that 3.745483... is irrational, while Allie says that it's rational. Who's right?
Cassidy is right because the number is a non-repeating and non-terminating decimal, which is irrational.
Solve.
The square root of 6 - the square root of 3.
0.717...
Solve:
the square root of 6 (the square root of 5)
5.477...
True or False:
the product of the square root of 3 and the square root of 3 is irrational.
Explain
False.
the product is 3, which is a whole number, the answer is rational
Is 2.6767 rational or irrational?Explain
Rational. Since it is a terminating decimal
Lia says that the square root of 64 is irrational. Her twin sister, Lexi says that its rational. Who is in the wrong? Explain
Lexi is correct because 8 is a rational number. 8 is a whole number/integer
Rational or irrational? Explain
the square root of 100 - the square root of 64
whole number/integer
Rational or irrational? Explain
square root of 30 times the square root of 5
Irrational because the product is a non-terminating and non-repeating decimal
True or false:
The product of two rational numbers is irrational.
Explain
False; two rational numbers = a rational number
Is the square root of 47 rational or irrational? Explain
Irrational.
47 is not a perfect square
or
it is an non-repeating and non-terminating decimal.
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 is non-repeating and non-terminating.
Rational or irrational? Explain
square root of three + square root of six
4.1815...
Irrational
Non-terminating and non-repeating decimal
Solve:
square root of 15 times square root of 2
5.4772...
True or false:
the sum of square root of 64 and the square root of 4 is rational.
Explain
True.
the sum is 10, which is a whole number.
Is the square root of 81 rational or irrational? Explain
Rational.
Since it is a perfect square number
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?
Eleanor is wrong because the product is 20, a rational number.
Rational or irrational? Explain
The square root of 16 + the square root of 4
6
Rational
Integer/whole number
Rational or irrational? Explain
the product of the square root of 25 and the square root of 4
Rational, because the product is a whole number/integer.
True or false?
The product of a rational number and a rational number leads to an rational number.
Explain
True.
Rational x rational = always rational