Chapter 4.3, Problem 100S

To determine

To calculate: The simplified form of the expression $2\sqrt{3}\cdot \sqrt{27}$ .

Answer to Problem 100S

The simplified form of the expression $2\sqrt{3}\cdot \sqrt{27}$ is $18$ .

Explanation of Solution

Given information:

The expression $2\sqrt{3}\cdot \sqrt{27}$ .

Formula used:

The product of $\sqrt{a}$ and $\sqrt{b}$ is denoted as $\sqrt{a}\cdot \sqrt{b}=\sqrt{ab}$ where a and b are positive integers.

Calculation:

Consider the expression $2\sqrt{3}\cdot \sqrt{27}$ .

Recall that product of $\sqrt{a}$ and $\sqrt{b}$ is denoted as $\sqrt{a}\cdot \sqrt{b}=\sqrt{ab}$ where a and b are positive integers.

Apply it,

  $\begin{array}{c}2\sqrt{3}\cdot \sqrt{27}=2\sqrt{3\left(27\right)}\\ =2\sqrt{3\cdot 3\cdot 9}\\ =2\cdot 3\cdot 3\\ =18\end{array}$

Thus, the simplified form of the expression $2\sqrt{3}\cdot \sqrt{27}$ is $18$ .