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Sagot :
[tex]\sqrt{48n^9}=\sqrt{16n^8\cdot3n}=\sqrt{16n^8}\cdot\sqrt{3n}=4n^4\sqrt{3n}[/tex]
Answer:
[tex]4n^4\sqrt{3n}[/tex]
Step-by-step explanation:
Use the exponent rules:
[tex]\sqrt[n]{x^a} = x^{\frac{a}{n}}[/tex]
[tex]\sqrt[n]{a^n} =a[/tex]
To find the simplified form of :
[tex]\sqrt{48n^9}[/tex]
We can write 48 and [tex]n^9[/tex] as:
[tex]48 = 4 \cdot 4 \cdot 3 = 4^2 \cdot 3[/tex]
[tex]n^9 = (n^4)^2 \cdot n[/tex]
then;
[tex]\sqrt{4^2 \cdot 3 \cdot (n^4)^2 \cdot n}[/tex]
Apply the exponent rule:
⇒[tex]4 \cdot n^4 \cdot \sqrt{3n}[/tex]
⇒[tex]4n^4\sqrt{3n}[/tex]
Therefore, the simplified form of square root 48n^9 is, [tex]4n^4\sqrt{3n}[/tex]
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