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Number Sense
Test lessons 58-63
Name: ________________________
Date: ________________
1. Draw all non-congruent rectangles with area 12. Explain why 12 is not a perfect square.
2. Write the factor rainbow of 16. Which factor is the square root? How do you know?
3. a) Find the prime factorization of 64 by first finding the prime factorization of its square root.
64
b) The prime number 2 occurs ___ times in the prime factorization of 64.
How many times will 2 occur in the prime factorization of 642? ____
4. a) The prime factorization of 12 is 2 × 2 × 3.
What is the prime factorization of 122 = 12 × 12? ______________________________
b) The prime number 2 occurs 6 times in the prime factorization of 64.
How many times will 2 occur in the prime factorization of 642? ____
Number Sense
Test lessons 58-63
Name: ________________________
Date: ________________
5. Decide whether or not 1575 is a perfect square by finding its prime factorization. Justify your
answer.
6. Evaluate.
a) 25  16
b)
64  16
c)
49  9
b)
9´ 4
7. Evaluate the two expressions. Then write = or ≠ in the box.
a.
25  9
25  9
9´ 4
Number Sense
Test lessons 58-63
Name: ________________________
Date: ________________
8. a) Which two consecutive whole numbers is
55 in between? ______ and ______
How do you know?
b) Explain why a square with area 55 cm2 does not have a whole number side length (in cm).
c) Estimate
55 to one decimal place by guessing, checking and revising. Show your work.
æ3ö
3 3
Bonus: ç ÷ =
´ =
2 2
è2ø
2
= ____ . ____ ____
1.52 = 1.5 × 1.5 = ____ . ____ ____
Compare your answers. Explain.