Question

$$1/2 \times 5 \sqrt{ 9-25/4 }$$

Answer

(5*sqrt(11))/4

Solution


Simplify  \(9-\frac{25}{4}\)  to  \(\frac{11}{4}\).
\[\frac{1}{2}\times 5\sqrt{\frac{11}{4}}\]
Simplify  \(\sqrt{\frac{11}{4}}\)  to  \(\frac{\sqrt{11}}{\sqrt{4}}\).
\[\frac{1}{2}\times 5\times \frac{\sqrt{11}}{\sqrt{4}}\]
Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[\frac{1}{2}\times 5\times \frac{\sqrt{11}}{2}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{1\times 5\sqrt{11}}{2\times 2}\]
Simplify  \(1\times 5\sqrt{11}\)  to  \(5\sqrt{11}\).
\[\frac{5\sqrt{11}}{2\times 2}\]
Simplify  \(2\times 2\)  to  \(4\).
\[\frac{5\sqrt{11}}{4}\]

Decimal Form: 4.145781