Estimating square roots activity with answers

A square root that is not a whole number still sits between two whole numbers.

• Recall perfect squares: 36, 49, 64, 81, 100, 144, 169, 196, 225, 256
• Find the squares just below and just above the number: 36 < 47 < 49
• Name the two roots: √47 is between 6 and 7
• Rule out pairs that are not next to each other, such as 7 and 9

Approximating square roots is 8.NS.A.2, a Grade 8 standard, so treat this page as an extension.

Before printing, list the squares from 1² to 16² together on scrap paper.

• Circle the number under the root sign.
• Find it between two squares on your list.
• Write the two roots, smaller first, or tick the matching pair.

Page two shows the eight answer pairs, from 2 and 3 for √5 up to 15 and 16 for √235.

• Halving the number: √200 is not 100; 14² = 196 and 15² = 225, so it lies between 14 and 15.
• Picking a pair with a gap: 7 and 9 surround √59, but the closest pair is 7 and 8.
• Mixing up the square and the root: 155 lies between 144 and 169, so the answer is 12 and 13.

Next, practice finding exact square roots of perfect squares.