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The area of a square is 64n^36 units. What is the side length of one side of the square? 8n^6 8n^18 64n^6 64n^18

Respuesta :

gmany

Answer:

[tex]\large\boxed{8n^{18}}[/tex]

Step-by-step explanation:

The formula of an area of a square:

[tex]A=s^2[/tex]

s - side length

We have

[tex]A=64n^{36}[/tex]

Method 1:

Substitute:

[tex]s^2=64n^{36}[/tex]

[tex]s^2=8^2n^{18\cdot2}[/tex]            use [tex](a^n)^m=a^{nm}[/tex]

[tex]s^2=8^2(n^{18})^2[/tex]         use [tex](ab)^n=a^nb^n[/tex]

[tex]s^2=(8n^{18})^2\to s=8n^{18}[/tex]

Method 2:

Substitute:

[tex]s^2=64n^{36}\to s=\sqrt{64n^{36}}[/tex]   use [tex]\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}[/tex]

[tex]s=\sqrt{64}\cdot\sqrt{n^{36}}[/tex]

[tex]s=8\sqrt{n^{(18)(2)}[/tex]     use [tex](a^n)^m=a^{nm}[/tex]

[tex]s=8\sqrt{(n^{18})^2}[/tex]      use [tex]\sqrt{a^2}=a[/tex] for [tex]a\geq0[/tex]

[tex]s=8n^{18}[/tex]

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