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Estimating Square Roots - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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Complexity=10

Between which two integers does the square root fall?
i.e. √15: Lower integer = 3, Higher integer = 4

 1 √35 Lower integer: Higher integer: 2 √10 Lower integer: Higher integer:

Complexity=12

Between which two integers does the square root fall?
i.e. √15: Lower integer = 3, Higher integer = 4

 1 √48 Lower integer: Higher integer: 2 √24 Lower integer: Higher integer:

Complexity=15

Between which two integers does the square root fall?
i.e. √15: Lower integer = 3, Higher integer = 4

 1 √33 Lower integer: Higher integer: 2 √18 Lower integer: Higher integer:

Complexity=20

Between which two integers does the square root fall?
i.e. √15: Lower integer = 3, Higher integer = 4

 1 √146 Lower integer: Higher integer: 2 √13 Lower integer: Higher integer:

Complexity=10

Between which two integers does the square root fall?
i.e. √15: Lower integer = 3, Higher integer = 4

135 Lower integer: Higher integer:
Solution
52 = 25
62 = 36
Since 35 is between these two numbers, √35 must be between 5 and 6.
To be exact, √35 = 5.9161
210 Lower integer: Higher integer:
Solution
32 = 9
42 = 16
Since 10 is between these two numbers, √10 must be between 3 and 4.
To be exact, √10 = 3.1623

Complexity=12

Between which two integers does the square root fall?
i.e. √15: Lower integer = 3, Higher integer = 4

148 Lower integer: Higher integer:
Solution
62 = 36
72 = 49
Since 48 is between these two numbers, √48 must be between 6 and 7.
To be exact, √48 = 6.9282
224 Lower integer: Higher integer:
Solution
42 = 16
52 = 25
Since 24 is between these two numbers, √24 must be between 4 and 5.
To be exact, √24 = 4.899

Complexity=15

Between which two integers does the square root fall?
i.e. √15: Lower integer = 3, Higher integer = 4

133 Lower integer: Higher integer:
Solution
52 = 25
62 = 36
Since 33 is between these two numbers, √33 must be between 5 and 6.
To be exact, √33 = 5.7446
218 Lower integer: Higher integer:
Solution
42 = 16
52 = 25
Since 18 is between these two numbers, √18 must be between 4 and 5.
To be exact, √18 = 4.2426

Complexity=20

Between which two integers does the square root fall?
i.e. √15: Lower integer = 3, Higher integer = 4

1146 Lower integer: Higher integer:
Solution
122 = 144
132 = 169
Since 146 is between these two numbers, √146 must be between 12 and 13.
To be exact, √146 = 12.083