Question

what is the answer to this?: 10√2-√3•√3•√3/√2

Answer 1

The answer is;

$\frac{20\sqrt[]{2}\text{ -3}\sqrt[]{6}}{2}$

Here, we want to evaluate the expression

We shall deal with the multiplication part first

We should understand this as regards surds;

$\begin{gathered} \sqrt[]{a}\text{ }\times\text{ }\sqrt[]{a\text{ }}\text{ = a} \\ a\text{ }\times\text{ }\sqrt[]{a}\text{ = a}\sqrt[]{a} \end{gathered}$

We proceed as follows;

$\begin{gathered} \sqrt[]{3}\text{ }\times\text{ }\sqrt[]{3}\text{ }\times\text{ }\sqrt[]{3}\text{ = 3}\sqrt[]{3} \\ \text{Thus, we have; }\frac{3\sqrt[]{3}}{\sqrt[]{2}} \end{gathered}$

We now proceed to subtract;

$\begin{gathered} 10\sqrt[]{2}\text{ - }\frac{3\sqrt[]{3}}{\sqrt[]{2}}=\frac{\sqrt[]{2\text{ }}(10\sqrt[]{2})-3\sqrt[]{3}}{\sqrt[]{2}}\text{ } \\ =\text{ }\frac{20-3\sqrt[]{3}}{\sqrt[]{2}} \\ \\ =\text{ }\frac{20\sqrt[]{2}\text{ -3}\sqrt[]{6}}{2}\text{ } \end{gathered}$

T