Question

$$\frac{1}{\sqrt{2}}\times\frac{\sqrt{3}}{2}-\frac{1}{\sqrt{2}}\times; \frac{1}{2}$$

Answer

8-1*sqrt(2)*;1/2

Solution


Simplify  \(\sqrt{32}\)  to  \(4\sqrt{2}\).
\[\begin{aligned}&1\times \sqrt{2}\times 4\sqrt{2}-1\times \sqrt{2}\\&\frac{1}{2}\end{aligned}\]
Simplify  \(1\times \sqrt{2}\times 4\sqrt{2}\)  to  \(4\sqrt{2\times 2}\).
\[\begin{aligned}&4\sqrt{2\times 2}-1\times \sqrt{2}\\&\frac{1}{2}\end{aligned}\]
Simplify  \(2\times 2\)  to  \(4\).
\[\begin{aligned}&4\sqrt{4}-1\times \sqrt{2}\\&\frac{1}{2}\end{aligned}\]
Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[\begin{aligned}&4\times 2-1\times \sqrt{2}\\&\frac{1}{2}\end{aligned}\]
Simplify  \(4\times 2\)  to  \(8\).
\[\begin{aligned}&8-1\times \sqrt{2}\\&\frac{1}{2}\end{aligned}\]