Respuesta :
Answer:
C. 64
Step-by-step explanation:
Hello there!
8*8=64, and 4*4*4=64, so C is correct.
:)
64 is both the square of an integer (8) and cube of an integer (4).
What is a square root of an integer?
"The square root of a number is a number that, when multiplied by itself, equals the desired value."
What is a cube root of an integer?
"The cube root of a number is product of a number multiplied by itself three times and is read as the number raised to the power 3."
We have
Option A
Number A = 121
A = 121
Apply square root for 121
= [tex]\sqrt{121}[/tex] = [tex]\sqrt{11^{2} }[/tex] = [tex]11[/tex]
Apply cube root for 121
= [tex]\sqrt[3]{121}[/tex] = [tex]\sqrt[3]{11.11}[/tex] = [tex]\sqrt[3]{11^{2} }[/tex]
∴ 121 is not an integer suitable for our condition.
Option B
Number B = 100
B = 100
Apply square root for 100
= [tex]\sqrt{100}[/tex] = [tex]\sqrt{10.10}[/tex] = [tex]\sqrt{10^{2} }[/tex] = [tex]10[/tex]
Apply cube root for 100
= [tex]\sqrt[3]{100}[/tex] = [tex]\sqrt[3]{10.10}[/tex] = [tex]\sqrt[3]{10^{2} }[/tex]
∴ 100 is not an integer suitable for our condition.
Option C
Number C = 64
C = 64
Apply square root for 64
= [tex]\sqrt{64}[/tex] = [tex]\sqrt{8.8}[/tex] = [tex]\sqrt{8^{2} }[/tex] = [tex]8[/tex] (integer)
Apply cube root for 64
= [tex]\sqrt[3]{64}[/tex] = [tex]\sqrt[3]{4.4.4}[/tex] = [tex]\sqrt[3]{4^{3} }[/tex] = [tex]4[/tex] (integer)
∴ 64 is an integer which is suitable for our condition
Option D
Number D = 16
D = 16
Apply square root for 16
= [tex]\sqrt{16}[/tex] = [tex]\sqrt{4.4}[/tex] = [tex]\sqrt{4^{2} }[/tex] = [tex]4[/tex]
Apply cube root for 16
= [tex]\sqrt[3]{16}[/tex] = [tex]\sqrt[3]{4.4}[/tex] = [tex]\sqrt[3]{4^{2} }[/tex]
∴ 16 is not an integer suitable for our condition
64 is both the square of an integer (8) and cube of an integer (4).
Learn more about square and cube root of an integer here
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