Name:___________________________________________ Date:___________________ Pd:_____
Exponents and Square Roots
Objective: Students will evaluate exponents and square roots.
Write a multiplication sentence to match each exponential expression.
1) 45 =
2) 36 =
3) 24 x 35 =
Put each of the following in exponential form.
4) 5 x 5 x 5 x 5 x 5 =
5) 6 x 6 x 6 =
6) 7 x 7 x 7 x 8 x 8 x 8 x 8 x 8 =
7) 2 x 3 x 4 x 3 x 2 x 2 x 4 x 3 x 2 =
Find the missing exponent.
8) 6x = 7,776
9) 10x = 100,000,000
10) 4x = 16,384
Evaluate.
11) What does (3 x 3)2 mean?
12) √49 =
13) √100 =
14) √144 =
15) √38 is between which whole numbers? How do you know?
a) 3 and 4
b) 4 and 5
c) 5 and 6
d) 6 and 7
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16) √4 x √4 =
17) Discuss the numerical value for #16. Why do you think this is the answer? How can you
generalize your finding to other problems?
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Name:___________________________________________ Date:___________________ Pd:_____
Exponents and Square Roots KEY
Write a multiplication sentence to match each exponential expression.
1) 45 = 1024
2) 36 = 729
3) 24 x 35 = 16 x 243 = 3,888
Put each of the following in exponential form.
4) 5 x 5 x 5 x 5 x 5 = 55
5) 6 x 6 x 6 = 63
6) 7 x 7 x 7 x 8 x 8 x 8 x 8 x 8 = 73 x 85
7) 2 x 3 x 4 x 3 x 2 x 2 x 4 x 3 x 2 = 24 x 33 x 42
Find the missing exponent.
8) 6x = 7,776 x = 5
9) 10x = 100,000,000 x = 8
10) 4x = 16,384 x = 7
Evaluate.
11) What does (3 x 3)2 mean? (3x3) x (3x3) or 34 or 9 x 9 or 81
12) √49 = 7
13) √100 = 10
14) √144 = 12
15) √38 is between which whole numbers? How do you know?
b) 3 and 4
b) 4 and 5
c) 5 and 6
d) 6 and 7
The square root of 36 is 6 and the square root of 49 is 7. Since 38 is between 36 and 49, the square
root is between 6 and 7.
16) √4 x √4 = 4
17) Discuss the numerical value for #16. Why do you think this is the answer? How can you
generalize your finding to other problems?The square root of 4 multiplied by the square root of
4 equals 4. The reason is that multiplying a square root by itself cancels out the square root as
squaring a number and taking the square root are inverse operations. The square root of any
number multiplied by itself will equal the number that is being square rooted.