Estimating Square Roots
Free printable worksheets for estimating square roots: find the two whole numbers each square root lies between, such as 6 and 7 for √40. Answer key included.
Each question gives the square root of a number that is not a perfect square, and asks for the two whole numbers it lies between. For √40, the perfect squares on either side are 36 and 49, so √40 is between √36 = 6 and √49 = 7.
The numbers go from 2 to 224, so the answers run from 1 and 2 up to 14 and 15, and no pair comes up twice on a page. The answer key gives the two whole numbers for each question.
What this worksheet covers
- Find the two whole numbers a square root lies between
- Use perfect squares to estimate a square root
Common Core standards
- 8.NS.A.2 Use rational approximations of irrational numbers to compare their size and estimate their value.
Frequently asked questions
How do you estimate a square root?
Find the perfect squares just below and just above the number. 70 lies between 64 and 81, so √70 lies between 8 and 9. To get closer, notice that 70 is much nearer 64, so √70 is a little over 8.
Why isn't √40 a whole number?
Because no whole number times itself makes 40: 6 × 6 is 36 and 7 × 7 is 49. Its square root is a decimal that never ends or repeats, about 6.32, which is why it is estimated rather than worked out exactly.
Is √50 closer to 7 or to 8?
To 7. 50 is only 1 more than 49 and 14 less than 64, so √50 is just over 7, about 7.07.
What grade is estimating square roots?
Eighth grade, as part of approximating irrational numbers. It needs the perfect squares first, which our square roots worksheets practise.