Question

I inserted a picture of the question, please please make it short, and yes i know the guidelines..

Answer 1

The square root of a number is usually written like this:

`\sqrt[]{289}`

Using the following property of radicals:

`\sqrt[n]{a^m}=a^{(m)/(n)}`

We can rewrite the square root of 289:

`\sqrt[]{289}=289^{(1)/(2)}`

On the other hand, when we calculate the square root of a number, we obtain two values, one positive and one negative.

`\begin{gathered} \sqrt[]{289}=17 \\ \text{ and} \\ \sqrt[]{289}=-17 \end{gathered}`

This happens because if we apply the inverse operation to each answer, which is squaring, we obtain the initial number.

`\begin{gathered} 17^2=(17)(17)=289 \\ \text{ and} \\ (-17)^2=(-17)(-17)=289 \end{gathered}`

Therefore, the square roots of 289 are:

`\begin{gathered} $$\boldsymbol{\sqrt[]{289}=289}^{\boldsymbol{(1)/(2)}}$$ \\ $$\boldsymbol{\sqrt[]{289}=17}$$ \\ $$\boldsymbol{\sqrt[]{289}=-17}$$ \end{gathered}`