Select an answer from the options below and click Submit.
Question 1
Indicate if the expression will simplify to a rational or an irrational value.
(65)2+1six fifths squared plus one
Answer: Correct! Go to question 2.
Answer: Incorrect. The answer is A.
This expression sums to 6125sixty one twenty fifths because
(65)2+1=(3625)+1=
3625+2525=6125six fifths squared plus one equals thirty six twenty fifths plus one equals thirty six twenty fifths plus twenty five twenty fifths equals sixty one twenty fifths.
This is a rational number because it is a number written as one integer divided by another.
Go to question 2.
Answer:Incorrect. Remember, a rational number is any number that can be written as one integer divided by another integer. Try again.
Question 2
Indicate if the expression will simplify to a rational or an irrational value.
4.3 + π3four and three tenths plus pi cubed
Answer: Correct! Go to question 3.
Answer: Incorrect. The answer is B. This expression includes pi (π), which cannot be written as one integer divided by another. Therefore, it is irrational. Go to question 3.
Answer:Incorrect. Remember, a rational number is any number that can be written as one integer divided by another integer. Try again.
Question 3
Indicate if the expression will simplify to a rational or an irrational value.
√5−2√3
the square root of five minus two times the square root of three
Answer: Correct! Go to question 4.
Answer: Incorrect. The answer is B. This expression includes √5the square root of 5 and √3the square root of 3. Neither of these values can be written as one integer divided by another; √5≈2.236067977…the square root of 5 is approximately equal to 2.236067977 and √3square root of 3≈1.732050808…and the square root of three is approximately equal to 1.732050808 Therefore, the value of the expression is irrational. Go to question 4.
Answer:Incorrect. Remember, a rational number is any number that can be written as one integer divided by another integer. Try again.
Question 4
Indicate if the expression will simplify to a rational or an irrational value.
π3pi divided by three
Answer: Correct! Go to question 5.
Answer: Incorrect. The answer is B. This expression includes pi (π), which cannot be written as one integer divided by another. Therefore, it is irrational. Go to question 5.
Answer:Incorrect. Remember, a rational number is any number that can be written as one integer divided by another integer. Try again.
Question 5
Indicate if the expression will simplify to a rational or an irrational value.
(√2square root of 2√3square root of 3)2the quotient of the square root of two and the square root of three squared
Answer: Correct! Go to question 6.
Answer: Incorrect. The answer is A. This expression simplifies to 23two thirds, since
(√2square root of 2√3square root of 3)2=
(√2square root of 2)2(√3square root of 3)2=23the quotient of the square root of two and the square root of three squared equals the square root of two squared divided by the square root of three squared which equals two over three.This product is written as one integer divided by another. Therefore, it is rational. Go to question 6.
Answer:Incorrect. Remember, a rational number is any number that can be written as one integer divided by another integer. Try again.
Question 6
Indicate if the expression will simplify to a rational or an irrational value.
0.6−0.3√4square root of 4The difference of sixth tenths repeated minus three tenths repeated divided by the square root of four
Answer: Correct!
Answer: Incorrect. The answer is A. This expression simplifies to 0.32three tenths repeated divided by two, which is equivalent to ⅓2one-third divided by two. This values simplifies to 16one sixth. The steps are shown below:
0.6−0.3√4square root of 4=0.32=⅓2=13⋅12=16The difference of sixth tenths repeated minus three tenths repeated divided by the square root of four equals three tenths repeated divided by two equals one third divided by two equals one third times one half equals one sixth
Since 16one sixth is written as one integer (1) divided by another (6), it is rational.
Answer:Incorrect. Remember, a rational number is any number that can be written as one integer divided by another integer. Try again.