√(1+1/10+(2700-5565 )^2/(381442500-10*(5565)^2 ))

asked by guest
on Apr 09, 2025 at 8:47 pm



You asked:

Evaluate the expression: 1+110+(2700−5565)2381442500−10⋅55652\sqrt{1 + \frac{1}{10} + \frac{{\left( 2700 - 5565 \right)}^{2}}{381442500 - 10 \cdot {5565}^{2}}}

MathBot Answer:

1+110+(2700−5565)2381442500−10⋅55652=17427312631889≈1.1019981623514436671288873657609\sqrt{1 + \frac{1}{10} + \frac{{\left( 2700 - 5565 \right)}^{2}}{381442500 - 10 \cdot {5565}^{2}}} = \frac{17 \sqrt{4273126}}{31889} \approx 1.1019981623514436671288873657609

1+110+(2700−5565)2381442500−10⋅55652=1+110+(2700−5565)2⋅1381442500−10⋅55652=1+110+(−2865)2⋅1381442500−10⋅55652=1+110+8208225⋅1381442500−10⋅55652=1+110+8208225⋅1381442500−10⋅30969225=1+110+8208225⋅1381442500−309692250=1+110+820822571750250=1+110+36481318890=1110+36481318890=3872631889=1731889⋅4273126\begin{aligned}\sqrt{1 + \frac{1}{10} + \frac{{\left( 2700 - 5565 \right)}^{2}}{381442500 - 10 \cdot {5565}^{2}}}&=\sqrt{1 + \frac{1}{10} + \left(2700 - 5565\right)^{2} \cdot \frac{1}{381442500 - 10 \cdot 5565^{2}}}\\&=\sqrt{1 + \frac{1}{10} + \left(-2865\right)^{2} \cdot \frac{1}{381442500 - 10 \cdot 5565^{2}}}\\&=\sqrt{1 + \frac{1}{10} + 8208225 \cdot \frac{1}{381442500 - 10 \cdot 5565^{2}}}\\&=\sqrt{1 + \frac{1}{10} + 8208225 \cdot \frac{1}{381442500 - 10 \cdot 30969225}}\\&=\sqrt{1 + \frac{1}{10} + 8208225 \cdot \frac{1}{381442500 - 309692250}}\\&=\sqrt{1 + \frac{1}{10} + \frac{8208225}{71750250}}\\&=\sqrt{1 + \frac{1}{10} + \frac{36481}{318890}}\\&=\sqrt{\frac{11}{10} + \frac{36481}{318890}}\\&=\sqrt{\frac{38726}{31889}}\\&=\frac{17}{31889} \cdot \sqrt{4273126}\end{aligned}

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