square root of 1.193 x 10^-8

asked by guest
on Jan 18, 2025 at 2:54 pm



You asked:

Evaluate the expression: 1.193⋅10−8\sqrt{1.193 \cdot {10}^{-8}}

MathBot Answer:

1.193⋅10−8=119301000000≈0.00010922453936730518434638072289\sqrt{1.193 \cdot {10}^{-8}} = \frac{\sqrt{11930}}{1000000} \approx 0.00010922453936730518434638072289

1.193⋅10−8=(1+1931000)⋅1108=11931000⋅1108=11931000⋅1100000000=1193100000000000=11000000⋅11930\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}

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