Question
\sqrt{\frac{49}{116}} simpliest form
Answers
GPT 3.5
To simplify $\sqrt{\frac{49}{116}}$ to simplest form, we can simplify the fraction under the square root sign, find the square root of the simplified fraction, and then simplify further if necessary.
First, let's simplify the fraction $\frac{49}{116}$. We can divide both the numerator and the denominator by the greatest common divisor, which is 1, to simplify the fraction:
$\frac{49}{116}$ ÷ $1$ ÷ $1$ = $\frac{49}{116}$.
Next, let's find the square root of $\frac{49}{116}$. Taking the square root of the numerator and the denominator separately, we get:
$\sqrt{\frac{49}{116}} = \frac{\sqrt{49}}{\sqrt{116}}$.
Since $\sqrt{49} = 7$ and $\sqrt{116}$ cannot be simplified further, we have:
$\frac{\sqrt{49}}{\sqrt{116}} = \frac{7}{\sqrt{116}}$.
To simplify further, we can rationalize the denominator. Multiplying both the numerator and the denominator by $\sqrt{116}$, we get:
$\frac{7}{\sqrt{116}} \times \frac{\sqrt{116}}{\sqrt{116}} = \frac{7\sqrt{116}}{116}$.
Since $\sqrt{116} = 2\sqrt{29}$, we have:
$\frac{7\sqrt{116}}{116} = \frac{7(2\sqrt{29})}{116} = \frac{14\sqrt{29}}{116}$.
To simplify even further, we can divide both the numerator and the denominator by the greatest common divisor, which is 2:
$\frac{14\sqrt{29}}{116}$ ÷ $2$ ÷ $2$ = $\frac{7\sqrt{29}}{58}$.
Therefore, $\sqrt{\frac{49}{116}}$ in simplest form is $\frac{7\sqrt{29}}{58}$.
First, let's simplify the fraction $\frac{49}{116}$. We can divide both the numerator and the denominator by the greatest common divisor, which is 1, to simplify the fraction:
$\frac{49}{116}$ ÷ $1$ ÷ $1$ = $\frac{49}{116}$.
Next, let's find the square root of $\frac{49}{116}$. Taking the square root of the numerator and the denominator separately, we get:
$\sqrt{\frac{49}{116}} = \frac{\sqrt{49}}{\sqrt{116}}$.
Since $\sqrt{49} = 7$ and $\sqrt{116}$ cannot be simplified further, we have:
$\frac{\sqrt{49}}{\sqrt{116}} = \frac{7}{\sqrt{116}}$.
To simplify further, we can rationalize the denominator. Multiplying both the numerator and the denominator by $\sqrt{116}$, we get:
$\frac{7}{\sqrt{116}} \times \frac{\sqrt{116}}{\sqrt{116}} = \frac{7\sqrt{116}}{116}$.
Since $\sqrt{116} = 2\sqrt{29}$, we have:
$\frac{7\sqrt{116}}{116} = \frac{7(2\sqrt{29})}{116} = \frac{14\sqrt{29}}{116}$.
To simplify even further, we can divide both the numerator and the denominator by the greatest common divisor, which is 2:
$\frac{14\sqrt{29}}{116}$ ÷ $2$ ÷ $2$ = $\frac{7\sqrt{29}}{58}$.
Therefore, $\sqrt{\frac{49}{116}}$ in simplest form is $\frac{7\sqrt{29}}{58}$.