6.4 More Accurately Estimate
Square Roots
Common Core Standards
8. NS.1 Know that there are numbers that are not rational, and
approximate them by rational numbers. Know that numbers that are not
rational are called irrational. Understand informally that every number
has a decimal expansion; for rational numbers show that the decimal
expansion repeats eventually, and convert a decimal expansion which
repeats eventually into a rational number.
8. NS.2 Use rational approximations of irrational numbers to compare
the size of irrational numbers, locate them approximately on a number
line diagram, and estimate the value of expressions (e.g., π 2). For
example, by truncating the decimal expansion of √2, show that √2 is
between 1 and 2, then between 1.4 and 1.5, and explain how to continue
on to get better approximations.
WARM-UP
Find the two whole numbers the square root falls between.
2) 63
1) 8
Round your answer to the nearest whole number.
4) 63
3) 8
0
1
2
3
4
5
6
7
8
9
10
More Accurately Estimate Square
Roots
Can we get closer to the actual answer
when estimating a square root.
6 = 2.449489743...
0
1
2
3
4
EXAMPLES
Round the square root to the nearest whole number.
98
18
0
1
2
3
4
5
6
7
8
9
10
EXAMPLES
Round the square root to the nearest whole number.
46
27
0
1
2
3
4
5
6
7
8
9
10
EXAMPLES
Which number is closest to the exact answer?
8 + 27
21
46
a)15
b)14
c)13
a)2
b)3
c) 4
NOTES
For better approximations we need to guess and check.
Examples
Round the square root to the nearest tenth.
46
27
4
5
6
7
8
EXAMPLES
Round the square root to the nearest tenth.
87
53
6
7
8
9
10
EXAMPLES
Which number is closest to the exact answer?
87 − 5
a) 4.1
b) 4.3
c) 4.9
PRACTICE
Round the square root to the nearest whole number.
135
20
0
1
2
3
4
5
6
7
8
9
10
PRACTICE
Round the square root to the nearest tenth.
33
5
70
6
7
8
9
FINAL QUESTION
Which number is closest to the exact answer?
π2
a)9.27
(use 3.14 for π)
b)9.86
c)10.24