(√7/4)(4/4)+(3/√7)(4/√7)

asked by guest
on Nov 26, 2024 at 12:51 am



You asked:

Evaluate the expression: \(\frac{\sqrt{7}}{4} \cdot \frac{4}{4} + \frac{3}{\sqrt{7}} \cdot \frac{4}{\sqrt{7}}\)

MathBot Answer:

\[\frac{\sqrt{7}}{4} \cdot \frac{4}{4} + \frac{3}{\sqrt{7}} \cdot \frac{4}{\sqrt{7}} = \frac{\sqrt{7}}{4} + \frac{12}{7} \approx 2.37572354205186193333968965269553\]

\[\begin{aligned}\frac{\sqrt{7}}{4} \cdot \frac{4}{4} + \frac{3}{\sqrt{7}} \cdot \frac{4}{\sqrt{7}}& = \sqrt{7} \cdot \frac{1}{4} \cdot \frac{4}{4} + 3 \cdot \frac{1}{\sqrt{7}} \cdot 4 \cdot \frac{1}{\sqrt{7}}\\& = \frac{1}{4} \cdot \sqrt{7} \cdot \frac{4}{4} + 3 \cdot \frac{1}{\sqrt{7}} \cdot 4 \cdot \frac{1}{\sqrt{7}}\\& = \frac{1}{4} \cdot \sqrt{7} + 3 \cdot \frac{1}{\sqrt{7}} \cdot 4 \cdot \frac{1}{\sqrt{7}}\\& = \frac{1}{4} \cdot \sqrt{7} + 3 \cdot \frac{1}{7} \cdot \sqrt{7} \cdot 4 \cdot \frac{1}{\sqrt{7}}\\& = \frac{1}{4} \cdot \sqrt{7} + 3 \cdot \frac{1}{7} \cdot \sqrt{7} \cdot \frac{4}{7} \cdot \sqrt{7}\\& = \frac{1}{4} \cdot \sqrt{7} + \frac{3}{7} \cdot \sqrt{7} \cdot \frac{4}{7} \cdot \sqrt{7}\\& = \frac{1}{4} \cdot \sqrt{7} + \frac{12}{7}\\& = \frac{12}{7} + \frac{1}{4} \cdot \sqrt{7}\end{aligned}\]

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