The square root of a number is usually written like this:
[tex]\sqrt[]{289}[/tex]
Using the following property of radicals:
[tex]\sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex]
We can rewrite the square root of 289:
[tex]\sqrt[]{289}=289^{\frac{1}{2}}[/tex]
On the other hand, when we calculate the square root of a number, we obtain two values, one positive and one negative.
[tex]\begin{gathered} \sqrt[]{289}=17 \\ \text{ and} \\ \sqrt[]{289}=-17 \end{gathered}[/tex]
This happens because if we apply the inverse operation to each answer, which is squaring, we obtain the initial number.
[tex]\begin{gathered} 17^2=(17)(17)=289 \\ \text{ and} \\ (-17)^2=(-17)(-17)=289 \end{gathered}[/tex]
Therefore, the square roots of 289 are:
[tex]\begin{gathered} $\boldsymbol{\sqrt[]{289}=289}^{\boldsymbol{\frac{1}{2}}}$ \\ $\boldsymbol{\sqrt[]{289}=17}$ \\ $\boldsymbol{\sqrt[]{289}=-17}$ \end{gathered}[/tex]
