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Arithmetic · Arithmetic

Evaluate (80 - 75)/sqrt(4^2/20 + 3^2/25)

\frac{80 - 75}{\sqrt{\frac{3^{2}}{25} + \frac{4^{2}}{20}}}

Step by step

  1. \frac{-75 + 80}{\sqrt{3^{2} \cdot \frac{1}{25} + 4^{2} \cdot \frac{1}{20}}} = \frac{5}{\sqrt{3^{2} \cdot \frac{1}{25} + 4^{2} \cdot \frac{1}{20}}}

    Add: -75 + 80 = 5.

  2. \frac{5}{\sqrt{3^{2} \cdot \frac{1}{25} + 4^{2} \cdot \frac{1}{20}}} = \frac{5}{\sqrt{3^{2} \cdot \frac{1}{25} + 16 \cdot \frac{1}{20}}}

    Power: 4^2 = 16.

  3. \frac{5}{\sqrt{3^{2} \cdot \frac{1}{25} + 16 \cdot \frac{1}{20}}} = \frac{5}{\sqrt{3^{2} \cdot \frac{1}{25} + \frac{4}{5}}}

    Multiply: 16(1/20) = 4/5.

  4. \frac{5}{\sqrt{3^{2} \cdot \frac{1}{25} + \frac{4}{5}}} = \frac{5}{\sqrt{9 \cdot \frac{1}{25} + \frac{4}{5}}}

    Power: 3^2 = 9.

  5. \frac{5}{\sqrt{9 \cdot \frac{1}{25} + \frac{4}{5}}} = \frac{5}{\sqrt{\frac{9}{25} + \frac{4}{5}}}

    Multiply: 9(1/25) = 9/25.

  6. \frac{5}{\sqrt{\frac{9}{25} + \frac{4}{5}}} = \frac{5}{\sqrt{\frac{9}{25} + \frac{20}{25}}}

    Rewrite every fraction over the common denominator 25.

  7. \frac{5}{\sqrt{\frac{9}{25} + \frac{20}{25}}} = \frac{5}{\sqrt{\frac{29}{25}}}

    Add: 9/25 + 20/25 = 29/25.

  8. \frac{5}{\sqrt{\frac{29}{25}}} = 5 \frac{5 \sqrt{29}}{29}

    Power: 1/(√(29/25)) = 5·√(29)/29.

  9. 5 \frac{5 \sqrt{29}}{29} = \frac{25 \sqrt{29}}{29}

    Multiply: 5(5·√(29)/29) = 25·√(29)/29.

Reveal the answer
\frac{25 \sqrt{29}}{29} \approx 4.6424