Question

review

1. circle the numbers that are perfect squares.

1 12 16 20
100 121 200 289
vocabulary builder
square root (noun) skwer root
definition: the square root of a number is a number that when multiplied by itself is equal to the given number.
using symbols: √16 = 4
using words: the square root of 16 is 4. it means, \i multiply 4 by itself to get 16.\
(example: √16 = 4 because 4² = 16)
use your vocabulary
use what you know about perfect squares and square roots to complete the table.

table (left):
number | number squared
1 | 1
2 | 4
3 | blank
4 | blank
5 | blank
blank | 36

table (right):
number | number squared
7 | 49
blank | 64
blank | 81
blank | blank
11 | blank
blank | blank

Explanation:

Part 1: Circle Perfect Squares

A perfect square is a number that is the square of an integer (e.g., \( n^2 \) where \( n \) is an integer).

• \( 1 = 1^2 \) → Perfect square.
• \( 12 \): No integer \( n \) with \( n^2 = 12 \) → Not a perfect square.
• \( 16 = 4^2 \) → Perfect square.
• \( 20 \): No integer \( n \) with \( n^2 = 20 \) → Not a perfect square.
• \( 100 = 10^2 \) → Perfect square.
• \( 121 = 11^2 \) → Perfect square.
• \( 200 \): No integer \( n \) with \( n^2 = 200 \) → Not a perfect square.
• \( 289 = 17^2 \) → Perfect square.

Part 2: Complete the Table (Number Squared)

To find "Number Squared," calculate \( n^2 \) (or find \( n \) if "Number Squared" is given, using \( n = \sqrt{\text{Number Squared}} \)).

Left Table (Number → Number Squared):

• \( 3 \): \( 3^2 = 9 \)
• \( 4 \): \( 4^2 = 16 \)
• \( 5 \): \( 5^2 = 25 \)
• "Number" for \( 36 \): \( \sqrt{36} = 6 \)

Right Table (Number → Number Squared / Number Squared → Number):

• "Number" for \( 64 \): \( \sqrt{64} = 8 \)
• "Number" for \( 81 \): \( \sqrt{81} = 9 \)
• Next number (after 9): \( 10 \), so \( 10^2 = 100 \)
• \( 11 \): \( 11^2 = 121 \)
• Next number (after 11): \( 12 \), so \( 12^2 = 144 \)

Final Table (Filled):

Number	Number Squared	Number	Number Squared
2	4	8	64
3	9	9	81
4	16	10	100
5	25	11	121
6	36	12	144

Final Answer (Perfect Squares to Circle):

Circle: \( \boldsymbol{1, 16, 100, 121, 289} \)

(Table filled as above.)

Answer:

Part 1: Circle Perfect Squares

A perfect square is a number that is the square of an integer (e.g., \( n^2 \) where \( n \) is an integer).

• \( 1 = 1^2 \) → Perfect square.
• \( 12 \): No integer \( n \) with \( n^2 = 12 \) → Not a perfect square.
• \( 16 = 4^2 \) → Perfect square.
• \( 20 \): No integer \( n \) with \( n^2 = 20 \) → Not a perfect square.
• \( 100 = 10^2 \) → Perfect square.
• \( 121 = 11^2 \) → Perfect square.
• \( 200 \): No integer \( n \) with \( n^2 = 200 \) → Not a perfect square.
• \( 289 = 17^2 \) → Perfect square.

Part 2: Complete the Table (Number Squared)

To find "Number Squared," calculate \( n^2 \) (or find \( n \) if "Number Squared" is given, using \( n = \sqrt{\text{Number Squared}} \)).

Left Table (Number → Number Squared):

• \( 3 \): \( 3^2 = 9 \)
• \( 4 \): \( 4^2 = 16 \)
• \( 5 \): \( 5^2 = 25 \)
• "Number" for \( 36 \): \( \sqrt{36} = 6 \)

Right Table (Number → Number Squared / Number Squared → Number):

• "Number" for \( 64 \): \( \sqrt{64} = 8 \)
• "Number" for \( 81 \): \( \sqrt{81} = 9 \)
• Next number (after 9): \( 10 \), so \( 10^2 = 100 \)
• \( 11 \): \( 11^2 = 121 \)
• Next number (after 11): \( 12 \), so \( 12^2 = 144 \)

Final Table (Filled):

Number	Number Squared	Number	Number Squared
2	4	8	64
3	9	9	81
4	16	10	100
5	25	11	121
6	36	12	144

Final Answer (Perfect Squares to Circle):

Circle: \( \boldsymbol{1, 16, 100, 121, 289} \)

(Table filled as above.)