## 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.
 62
Lower integer: Higher integer: 2.
 75
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.
 51
Lower integer: Higher integer: 2.
 43
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.
 23
Lower integer: Higher integer: 2.
 238
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.
 14
Lower integer: Higher integer: 2.
 86
Lower integer: Higher integer:

## Answers

### Complexity=10

Between which two integers does the square root fall?
i.e. √15: Lower integer = 3, Higher integer = 4
#ProblemCorrect AnswerYour Answer
1
 62
Lower integer: Higher integer:
Solution
72 = 49
82 = 64
Since 62 is between these two numbers,
 62
must be between 7 and 8.
To be exact,
 62
= 7.874
#ProblemCorrect AnswerYour Answer
2
 75
Lower integer: Higher integer:
Solution
82 = 64
92 = 81
Since 75 is between these two numbers,
 75
must be between 8 and 9.
To be exact,
 75
= 8.6603

### Complexity=12

Between which two integers does the square root fall?
i.e. √15: Lower integer = 3, Higher integer = 4
#ProblemCorrect AnswerYour Answer
1
 51
Lower integer: Higher integer:
Solution
72 = 49
82 = 64
Since 51 is between these two numbers,
 51
must be between 7 and 8.
To be exact,
 51
= 7.1414
#ProblemCorrect AnswerYour Answer
2
 43
Lower integer: Higher integer:
Solution
62 = 36
72 = 49
Since 43 is between these two numbers,
 43
must be between 6 and 7.
To be exact,
 43
= 6.5574

### Complexity=15

Between which two integers does the square root fall?
i.e. √15: Lower integer = 3, Higher integer = 4
#ProblemCorrect AnswerYour Answer
1
 23
Lower integer: Higher integer:
Solution
42 = 16
52 = 25
Since 23 is between these two numbers,
 23
must be between 4 and 5.
To be exact,
 23
= 4.7958
#ProblemCorrect AnswerYour Answer
2
 238
Lower integer: Higher integer:
Solution
152 = 225
162 = 256
Since 238 is between these two numbers,
 238
must be between 15 and 16.
To be exact,
 238
= 15.4272

### Complexity=20

Between which two integers does the square root fall?
i.e. √15: Lower integer = 3, Higher integer = 4
#ProblemCorrect AnswerYour Answer
1
 14
Lower integer: Higher integer:
Solution
32 = 9
42 = 16
Since 14 is between these two numbers,
 14
must be between 3 and 4.
To be exact,
 14
= 3.7417
#ProblemCorrect AnswerYour Answer
2
 86
Lower integer: Higher integer:
Solution
92 = 81
102 = 100
Since 86 is between these two numbers,
 86
must be between 9 and 10.
To be exact,
 86
= 9.2736
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