square root of 1.193 x 10^-8
You asked:
Evaluate the expression: \(\sqrt{1.193 \cdot {10}^{-8}}\)
MathBot Answer:
\[\sqrt{1.193 \cdot {10}^{-8}} = \frac{\sqrt{11930}}{1000000} \approx 0.00010922453936730518434638072289\]
\[\begin{aligned}\sqrt{1.193 \cdot {10}^{-8}}& = \sqrt{\left(1 + \frac{193}{1000}\right) \cdot \frac{1}{10^{8}}}\\& = \sqrt{\frac{1193}{1000} \cdot \frac{1}{10^{8}}}\\& = \sqrt{\frac{1193}{1000} \cdot \frac{1}{100000000}}\\& = \sqrt{\frac{1193}{100000000000}}\\& = \frac{1}{1000000} \cdot \sqrt{11930}\end{aligned}\]