Extra Set

Grade 8 · Unit 6 · L25 · Version A · E222

Rational approximations of irrationals

Name ________________

Date ________________

Period ________________

1.
Between which two consecutive integers does √2 lie?
Answer. 1 and 2
1² = 1 and 2² = 4, and 1 < 2 < 4.
2.
Between which two consecutive integers does √10 lie?
Answer. 3 and 4
3² = 9 and 4² = 16, and 9 < 10 < 16.
3.
Between which two consecutive integers does √5 lie?
Answer. 2 and 3
2² = 4 and 3² = 9, and 4 < 5 < 9.
4.
Between which two consecutive integers does √11 lie?
Answer. 3 and 4
3² = 9 and 4² = 16, and 9 < 11 < 16.
5.
Between which two consecutive integers does √7 lie? Then Jonah needs 3 of that amount. What is the total they need?
Answer. 6 and 3
2² = 4 and 3² = 9, and 4 < 7 < 9. Then multiply by 3: 6 and 3.
6.
Between which two consecutive integers does √2 lie? Then Grace needs 3 of that amount. What is the total they need?
Answer. 3 and 2
1² = 1 and 2² = 4, and 1 < 2 < 4. Then multiply by 3: 3 and 2.
7.
Between which two consecutive integers does √5 lie? Then Luis needs 5 of that amount. What is the total they need?
Answer. 10 and 3
2² = 4 and 3² = 9, and 4 < 5 < 9. Then multiply by 5: 10 and 3.
8.
Between which two consecutive integers does √11 lie? Then Ava needs 2 of that amount. What is the total they need?
Answer. 6 and 4
3² = 9 and 4² = 16, and 9 < 11 < 16. Then multiply by 2: 6 and 4.
9.
Between which two consecutive integers does √2 lie? Then Elena needs 5 of that amount. What is the total they need?
Answer. 5 and 2
1² = 1 and 2² = 4, and 1 < 2 < 4. Then multiply by 5: 5 and 2.
10.
Between which two consecutive integers does √10 lie? Then Priya needs 4 of that amount. What is the total they need?
Answer. 12 and 4
3² = 9 and 4² = 16, and 9 < 10 < 16. Then multiply by 4: 12 and 4.
11.
Think
Mei tried this problem:
Between which two consecutive integers does √2 lie?
Mei wrote 2 and 2. That is not correct. What is the right answer?
Answer. 1 and 2
Mei’s answer 2 and 2 is off. 1² = 1 and 2² = 4, and 1 < 2 < 4.
12.
Think
Owen tried this problem:
Between which two consecutive integers does √10 lie?
Owen wrote -3 and 4. That is not correct. What is the right answer?
Answer. 3 and 4
Owen’s answer -3 and 4 is off. 3² = 9 and 4² = 16, and 9 < 10 < 16.

Original extra practice. Keys are computed from the items, not guessed.

L25 · Rational approximations of irrationals