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Square Roots Approximating Between Perfect Square Roots (Level 3)

This math topic focuses on approximating square roots between perfect square roots at an advanced level. It involves identifying the closest perfect square roots that are just smaller and larger than the square root of a non-perfect-square number. Learners practice pinpointing these boundaries by considering numbers like 87, 72, 28, 137, 107, 156, and 154, determining the perfect squares that lie immediately below and above their square roots. The exercises enhance understanding of squares and square roots, refining estimation skills and familiarity with square number properties.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Square Roots Approximating Between Perfect Square Roots

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

Find the closest perfect square roots above and below the given square root

?<151<?\sqrt{?} < \sqrt{151} < \sqrt{?}

Square Roots Approximating Between Perfect Square Roots Worksheet

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Math worksheet on 'Square Roots Approximating Between Perfect Square Roots (Level 3)'. Part of a broader unit on 'Squares and Square Roots - Advanced' Learn online: app.mobius.academy/math/units/squares_and_square_roots_advanced/
1
Find the closest perfect square roots above and below the given square root
A LaTex expression showing square root of ? < square root of 107 < square root of ?
a
100, 144
b
96, 129
c
100, 121
d
104, 115
e
102, 125
f
104, 117
2
Find the closest perfect square roots above and below the given square root
A LaTex expression showing square root of ? < square root of 76 < square root of ?
a
64, 81
b
68, 81
c
62, 81
d
60, 79
e
66, 91
f
60, 77
3
Find the closest perfect square roots above and below the given square root
A LaTex expression showing square root of ? < square root of 127 < square root of ?
a
121, 146
b
121, 142
c
121, 144
d
117, 142
e
123, 156
f
100, 144
4
Find the closest perfect square roots above and below the given square root
A LaTex expression showing square root of ? < square root of 159 < square root of ?
a
144, 185
b
121, 169
c
144, 169
d
148, 175
e
148, 167
f
144, 175
5
Find the closest perfect square roots above and below the given square root
A LaTex expression showing square root of ? < square root of 135 < square root of ?
a
121, 142
b
121, 144
c
123, 142
d
121, 152
e
121, 169
f
125, 160
6
Find the closest perfect square roots above and below the given square root
A LaTex expression showing square root of ? < square root of 162 < square root of ?
a
144, 169
b
144, 196
c
144, 173
d
144, 171
e
146, 187
f
140, 163
7
Find the closest perfect square roots above and below the given square root
A LaTex expression showing square root of ? < square root of 129 < square root of ?
a
121, 144
b
125, 144
c
119, 138
d
123, 144
e
121, 169
f
121, 138