Chapter R7, Problem 1E

To determine

Simplify the expression $\sqrt{3}\cdot \sqrt{3}$ .

Answer to Problem 1E

Solution: The simplified value of given expression is $\text{3}$ .

Explanation of Solution

Given: The given expression is $\sqrt{3}\cdot \sqrt{3}$ .

Concept used: Given expression can be simplified using the property $\sqrt{a}\cdot \sqrt{b}=\sqrt{ab}$ for $a,b\ge 0$ .

Calculation: Consider the expression $\sqrt{3}.\sqrt{3}$ .

Since $3>0$ , we can use property $\sqrt{a}\cdot \sqrt{b}=\sqrt{ab}$ for $a,b\ge 0$ to simply the given expression.

  $\begin{array}{l}\sqrt{3}.\sqrt{3}\\ =\sqrt{3\cdot 3}\\ =\sqrt{9}\\ =3\end{array}$

Therefore, $\sqrt{3}\cdot \sqrt{3}=3$

Conclusion:

The simplification value of the given expression is $\sqrt{3}\cdot \sqrt{3}=3$ .