Checkpoint: squares, the staircase and roots

A block of tiles is 6 across and 6 down. How many tiles is that?

• 66, because the two sixes sit side by side
• 36
• 12, because 6 + 6 = 12

A square 8 tiles across grows to 9 tiles across. How many tiles does the new layer hold?

• 17
• 9, because the new side is 9
• 2, because the side went up by one

Which number can its last digit rule out as a square?

• 45, because it is not even
• 63, because it ends in 3
• 81, because it is odd

What is the square root of 49?

• 2401, because that is 49 squared
• 24.5, because that is half of 49
• 7

144 is 2 × 2 × 2 × 2 × 3 × 3. What is its square root?

• 12
• 10, because 4 + 3 + 3 = 10
• 144, because you multiply all six primes