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Simplify the following radical sqrt 300 x^15

1 Answer

3 votes

Answer:


\large\boxed{\sqrt{300x^(15)}=10x^7√(3x)}

Explanation:


Domain: x\geq0\\\\\sqrt{300x^(15)}=\sqrt{100\cdot3\cdot x^(14+1)}\\\\\text{use}\ a^n\cdot a^m=a^(n+m)\\\\=\sqrt{100\cdot3\cdot x^(14)\cdot x^1}\\\\\text{use}\ √(ab)=√(a)\cdot√(b)\\\\=√(100)\cdot\sqrt3\cdot\sqrt{x^(14)}\cdot√(x)=10\cdot\sqrt3\cdot\sqrt{x^(7\cdot2)}\cdot√(x)\\\\\text{use}\ (a^n)^m=a^(nm)\\\\=10\cdot\sqrt3\cdot√((x^7)^2)\cdot√(x)\\\\\text{use}\ √(a^2)=a\ \text{for}\ a\geq0\\\\=10\cdot\sqrt3\cdot x^7\cdot√(x)=10x^7√(3x)

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