\frac{4^{\frac{1}{2}}\cdot \left(5.64\right)^{\frac{1}{2}}}{5^{\frac{1}{2}}}

asked by guest
on Nov 15, 2024 at 12:39 pm



You asked:

Evaluate the expression: 412⋅5.6412512\frac{{4}^{\frac{1}{2}} \cdot {5.64}^{\frac{1}{2}}}{{5}^{\frac{1}{2}}}

MathBot Answer:

412⋅5.6412512=270525≈2.12414688757628058719742875409242\frac{{4}^{\frac{1}{2}} \cdot {5.64}^{\frac{1}{2}}}{{5}^{\frac{1}{2}}} = \frac{2 \sqrt{705}}{25} \approx 2.12414688757628058719742875409242

412⋅5.6412512=4⋅5+64100⋅15=2⋅5+64100⋅15=2⋅5+1625⋅15=2⋅14125⋅15=2⋅15⋅141⋅15=2⋅125⋅705=225⋅705\begin{aligned}\frac{{4}^{\frac{1}{2}} \cdot {5.64}^{\frac{1}{2}}}{{5}^{\frac{1}{2}}}&=\sqrt{4} \cdot \sqrt{5 + \frac{64}{100}} \cdot \frac{1}{\sqrt{5}}\\&=2 \cdot \sqrt{5 + \frac{64}{100}} \cdot \frac{1}{\sqrt{5}}\\&=2 \cdot \sqrt{5 + \frac{16}{25}} \cdot \frac{1}{\sqrt{5}}\\&=2 \cdot \sqrt{\frac{141}{25}} \cdot \frac{1}{\sqrt{5}}\\&=2 \cdot \frac{1}{5} \cdot \sqrt{141} \cdot \frac{1}{\sqrt{5}}\\&=2 \cdot \frac{1}{25} \cdot \sqrt{705}\\&=\frac{2}{25} \cdot \sqrt{705}\end{aligned}

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