Tidying messy roots

Mathematics · Number Representation & Place Value · ages 15-16

Name ______________________ Date ____________

What is √50 in simplest surd form?
- 5√2
- 25√2
- 10√5
- 2√5
What is root 50 in simplest surd form?
- 25 root 2
- 5 root 2
- 2 root 5
Root 2 plus root 3 makes root 5.
Circle one: True False
Root 72 simplifies to a root 2, where a is a whole number. What is a?
Answer: ______________
What is 6 over root 2 with a rational denominator?
- 6 root 2
- root 3
- 3 root 2
What is 6/√2 with a rational denominator?
- 3√2
- 6√2
- √3
- 3
What is √2 × (√8 + √2)?
- 6
- 8
- 4 + 2√2
- 2√10
What is root 2 times (root 8 + root 2)?
Answer: ______________
Which sum can combine into a single surd?
- Root 2 + root 3
- 3 root 7 + 4 root 7
- Root 5 + root 11
10 over root 5 rationalises to a root 5, where a is whole. What is a?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

5√2 · 50 = 25 × 2, and √25 = 5, so √50 = 5√2.
5 root 2 · 50 = 25 times 2, and root 25 = 5, so root 50 = 5 root 2.
False · Only matching roots merge. Root 2 plus root 3 cannot combine.
6 · 72 = 36 times 2, and root 36 = 6, so a = 6.
3 root 2 · Multiply top and bottom by root 2: 6 root 2 over 2 = 3 root 2.
3√2 · Multiply top and bottom by √2 to get 6√2/2, which simplifies to 3√2.
6 · √2 × √8 = √16 = 4 and √2 × √2 = 2, so the total is 6.
6 · Root 2 times root 8 is 4, and root 2 times root 2 is 2, giving 6.
3 root 7 + 4 root 7 · Only matching roots merge: 3 root 7 + 4 root 7 = 7 root 7.
2 · Multiply top and bottom by root 5: 10 root 5 over 5 = 2 root 5.