√30: 5² = 25 and 6² = 36, and 30 is between them. So √30 is between 5 and 6. 30 is 5 above 25 and 6 below 36, so √30 is a little closer to 5.
Worked example
√37 is between which two whole numbers?
Answer:6 and 7
The best choice is 6 and 7. Right: 6² = 36 and 7² = 49, and 37 is between them. Find the two perfect squares (or cubes) just below and above the number.
For grown-ups: Irrational numbers; decimal approximations. Below: three problems to try with the worked answers, and a free printable sheet. Children can practise the same skill as a game, with no sign-up and no ads.
CCSS 8.NS.A.1–2
What this practises, for teachers
Practices irrational numbers; decimal approximations (8.NS.A.1–2). A printable sheet with its answer key, worked answers on the page, no accounts.
The best choice is 6 and 7. Right: 6² = 36 and 7² = 49, and 38 is between them. Find the two perfect squares (or cubes) just below and above the number.
Which whole number is √55 closest to?
Show the answer and how
Answer:7
Find the squares on each side: 7² = 49 and 8² = 64. 55 is closer to 49, so √55 is closest to 7. Answer: 7.
Estimate √77 to the nearest tenth. (Hint: try squaring numbers with one decimal place.)
Show the answer and how
Answer:8.8
√77 is between 8 and 9. Try tenths: 8.7² = 75.69 and 8.8² = 77.44, so it is between those. The halfway number is 8.75, and 8.75² = 76.5625. 77 is more than that, so √77 is closer to 8.8. So √77 ≈ 8.8. Answer: 8.8.