Square Root Tricks (1)

Step 1: Find the perfect square nearest to 173.

$\large 13^2 =169$

Step 2: Divide 173 by $\sqrt{169} = 13$

$\large \frac{173}{13}$

Step 3: Find the average of $\dfrac{173}{13}$ and $\sqrt{169} =13$

$\large \frac{\frac{173}{13} + 13}2 = \dfrac{\frac{173 + 169}{13}}2 = \dfrac{\frac{342}{13}}2 = \dfrac{342}{26} = \dfrac{171}{13} \approx 13.15$

Hence $\sqrt{173} \approx 13.15$