Calculating Square Root of Mixed Fraction
To find the square root of the mixed fraction $5\frac{44}{49}$, follow these steps:
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Convert to Improper Fraction:
First, convert the mixed fraction $5\frac{44}{49}$ into an improper fraction.
$5\frac{44}{49} = \frac{(5 \times 49) + 44}{49} = \frac{245 + 44}{49} = \frac{289}{49}$
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Find the Square Root:
Now, calculate the square root of the improper fraction obtained.
$\sqrt{5\frac{44}{49}} = \sqrt{\frac{289}{49}}$
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Simplify the Square Root:
The square root of a fraction is the square root of the numerator divided by the square root of the denominator.
$\sqrt{\frac{289}{49}} = \frac{\sqrt{289}}{\sqrt{49}}$
We know that $17 \times 17 = 289$ and $7 \times 7 = 49$. Therefore,
$\frac{\sqrt{289}}{\sqrt{49}} = \frac{17}{7}$
The square root of $5\frac{44}{49}$ is $\frac{17}{7}$.
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