Let’s solve this step by step.
We are asked to estimate square roots — that means we need to find two whole numbers that the square root falls between. For example, √10 is between 3 and 4 because 3² = 9 and 4² = 16, and 10 is between 9 and 16.
We’ll go one by one:
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√110 → What perfect squares are near 110?
10² = 100, 11² = 121 → So √110 is between
10 and
11
√12 → 3² = 9, 4² = 16 → Between
3 and
4
√75 → 8² = 64, 9² = 81 → Between
8 and
9
√52 → 7² = 49, 8² = 64 → Between
7 and
8
√98 → 9² = 81, 10² = 100 → Between
9 and
10
√178 → 13² = 169, 14² = 196 → Between
13 and
14
√6 → 2² = 4, 3² = 9 → Between
2 and
3
√266 → 16² = 256, 17² = 289 → Between
16 and
17
√46 → 6² = 36, 7² = 49 → Between
6 and
7
√84 → 9² = 81, 10² = 100 → Between
9 and
10
√215 → 14² = 196, 15² = 225 → Between
14 and
15
√250 → 15² = 225, 16² = 256 → Between
15 and
16
√7 → 2² = 4, 3² = 9 → Between
2 and
3
√3 → 1² = 1, 2² = 4 → Between
1 and
2
√274 → 16² = 256, 17² = 289 → Between
16 and
17
√21 → 4² = 16, 5² = 25 → Between
4 and
5
√10 → 3² = 9, 4² = 16 → Between
3 and
4
√18 → 4² = 16, 5² = 25 → Between
4 and
5
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Now let’s write all answers in order as they appear on the worksheet (left column first, then right column):
Left Column:
√110 → 10, 11
√75 → 8, 9
√98 → 9, 10
√6 → 2, 3
√46 → 6, 7
√215 → 14, 15
√7 → 2, 3
√274 → 16, 17
√10 → 3, 4
Right Column:
√12 → 3, 4
√52 → 7, 8
√178 → 13, 14
√266 → 16, 17
√84 → 9, 10
√250 → 15, 16
√3 → 1, 2
√21 → 4, 5
√18 → 4, 5
Final Answer:
√110 is between 10 and 11
√12 is between 3 and 4
√75 is between 8 and 9
√52 is between 7 and 8
√98 is between 9 and 10
√178 is between 13 and 14
√6 is between 2 and 3
√266 is between 16 and 17
√46 is between 6 and 7
√84 is between 9 and 10
√215 is between 14 and 15
√250 is between 15 and 16
√7 is between 2 and 3
√3 is between 1 and 2
√274 is between 16 and 17
√21 is between 4 and 5
√10 is between 3 and 4
√18 is between 4 and 5
Parent Tip: Review the logic above to help your child master the concept of estimate square root worksheet.
