\sqrt{(-1 - (-0.1339745962))^2 + (-1 - (-1.482))^2 + (4 - 3.433)^2}

asked by guest
on Oct 21, 2024 at 7:47 pm



You asked:

Evaluate the expression: \(\sqrt{{\left( -1 - -0.1339745962 \right)}^{2} + {\left( -1 - -1.482 \right)}^{2} + {\left( 4 - 3.433 \right)}^{2}}\)

MathBot Answer:

\[\sqrt{{\left( -1 - -0.1339745962 \right)}^{2} + {\left( -1 - -1.482 \right)}^{2} + {\left( 4 - 3.433 \right)}^{2}} = \frac{\sqrt{32595325000673826361}}{5000000000} \approx 1.14184631191196350706094393196717\]

\[\begin{aligned}\sqrt{{\left( -1 - -0.1339745962 \right)}^{2} + {\left( -1 - -1.482 \right)}^{2} + {\left( 4 - 3.433 \right)}^{2}}& = \sqrt{\left(-1 - - \frac{1339745962}{10000000000}\right)^{2} + \left(-1 - - \left(1 + \frac{482}{1000}\right)\right)^{2} + \left(4 - \left(3 + \frac{433}{1000}\right)\right)^{2}}\\& = \sqrt{\left(-1 - - \frac{669872981}{5000000000}\right)^{2} + \left(-1 - - \left(1 + \frac{482}{1000}\right)\right)^{2} + \left(4 - \left(3 + \frac{433}{1000}\right)\right)^{2}}\\& = \sqrt{\left(-1 + \frac{669872981}{5000000000}\right)^{2} + \left(-1 - - \left(1 + \frac{482}{1000}\right)\right)^{2} + \left(4 - \left(3 + \frac{433}{1000}\right)\right)^{2}}\\& = \sqrt{\left(- \frac{4330127019}{5000000000}\right)^{2} + \left(-1 - - \left(1 + \frac{482}{1000}\right)\right)^{2} + \left(4 - \left(3 + \frac{433}{1000}\right)\right)^{2}}\\& = \sqrt{\frac{18750000000673826361}{25000000000000000000} + \left(-1 - - \left(1 + \frac{482}{1000}\right)\right)^{2} + \left(4 - \left(3 + \frac{433}{1000}\right)\right)^{2}}\\& = \sqrt{\frac{18750000000673826361}{25000000000000000000} + \left(-1 - - \left(1 + \frac{241}{500}\right)\right)^{2} + \left(4 - \left(3 + \frac{433}{1000}\right)\right)^{2}}\\& = \sqrt{\frac{18750000000673826361}{25000000000000000000} + \left(-1 - - \frac{741}{500}\right)^{2} + \left(4 - \left(3 + \frac{433}{1000}\right)\right)^{2}}\\& = \sqrt{\frac{18750000000673826361}{25000000000000000000} + \left(-1 + \frac{741}{500}\right)^{2} + \left(4 - \left(3 + \frac{433}{1000}\right)\right)^{2}}\\& = \sqrt{\frac{18750000000673826361}{25000000000000000000} + \left(\frac{241}{500}\right)^{2} + \left(4 - \left(3 + \frac{433}{1000}\right)\right)^{2}}\\& = \sqrt{\frac{18750000000673826361}{25000000000000000000} + \frac{58081}{250000} + \left(4 - \left(3 + \frac{433}{1000}\right)\right)^{2}}\\& = \sqrt{\frac{18750000000673826361}{25000000000000000000} + \frac{58081}{250000} + \left(4 - \frac{3433}{1000}\right)^{2}}\\& = \sqrt{\frac{18750000000673826361}{25000000000000000000} + \frac{58081}{250000} + \left(\frac{567}{1000}\right)^{2}}\\& = \sqrt{\frac{18750000000673826361}{25000000000000000000} + \frac{58081}{250000} + \frac{321489}{1000000}}\\& = \sqrt{\frac{24558100000673826361}{25000000000000000000} + \frac{321489}{1000000}}\\& = \sqrt{\frac{32595325000673826361}{25000000000000000000}}\\& = \frac{1}{5000000000} \cdot \sqrt{32595325000673826361}\end{aligned}\]

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