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raketka [301]
2 years ago
9

Simplify this radical. Square root of x to the 13th power

Mathematics
2 answers:
wlad13 [49]2 years ago
8 0

Answer:

x^6\sqrt{x}

Step-by-step explanation:

we have:

\sqrt{x^{13}}

we can write:

\sqrt{x^{13}} :\sqrt{x^{2}*x^{2}*x^{2}*x^{2}*x^{2}*x^{2}*x}

we know:

\sqrt{x^{2}} = x

so we have:

\sqrt{x^{13}} =\sqrt{x^{2}*x^{2}*x^{2}*x^{2}*x^{2}*x^{2}*x}

we have:

\sqrt{x^{2}*x^{2}*x^{2}*x^{2}*x^{2}*x^{2}*x}=

x^{6} \sqrt{x}

Lubov Fominskaja [6]2 years ago
8 0

Answer:

\large\boxed{\sqrt{x^{13}}=x^6\sqrt{x}}

Step-by-step explanation:

\sqrt{x^{13}}=\sqrt{x^{12+1}}\qquad\text{use}\ a^na^m=a^{n+m}\\\\=\sqrt{x^{12}x^1}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{x^{12}}\cdot\sqrt{x}=\sqrt{x^{6\cdot2}}\cdot\sqrt{x}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=\sqrt{(x^6)^2}\cdot\sqrt{x}\qquad\text{use}\ \sqrt{x^2}=|x|\\\\=|x^6|\sqrt{x}=x^6\sqrt{x}\ \text{because}\ x^6\geq0

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