√(28.8² + 114.12²)

asked by guest
on Jan 14, 2025 at 7:05 am



You asked:

Evaluate the expression: 28.82+114.122\sqrt{{28.8}^{2} + {114.12}^{2}}

MathBot Answer:

28.82+114.122=910688925≈117.69797959183496536389708855032563\sqrt{{28.8}^{2} + {114.12}^{2}} = \frac{9 \sqrt{106889}}{25} \approx 117.69797959183496536389708855032563

28.82+114.122=(28+810)2+(114+12100)2=(28+45)2+(114+12100)2=(1445)2+(114+12100)2=2073625+(114+12100)2=2073625+(114+325)2=2073625+(285325)2=2073625+8139609625=8658009625=925⋅106889\begin{aligned}\sqrt{{28.8}^{2} + {114.12}^{2}}&=\sqrt{\left(28 + \frac{8}{10}\right)^{2} + \left(114 + \frac{12}{100}\right)^{2}}\\&=\sqrt{\left(28 + \frac{4}{5}\right)^{2} + \left(114 + \frac{12}{100}\right)^{2}}\\&=\sqrt{\left(\frac{144}{5}\right)^{2} + \left(114 + \frac{12}{100}\right)^{2}}\\&=\sqrt{\frac{20736}{25} + \left(114 + \frac{12}{100}\right)^{2}}\\&=\sqrt{\frac{20736}{25} + \left(114 + \frac{3}{25}\right)^{2}}\\&=\sqrt{\frac{20736}{25} + \left(\frac{2853}{25}\right)^{2}}\\&=\sqrt{\frac{20736}{25} + \frac{8139609}{625}}\\&=\sqrt{\frac{8658009}{625}}\\&=\frac{9}{25} \cdot \sqrt{106889}\end{aligned}

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