Chapter 1.1, Problem 21PPS

To determine

To evaluate: the given expression

Answer to Problem 21PPS

The numerical value of the given expression is 62.

Explanation of Solution

Given:

  $2\left[3+7\left(4\right)\right]$

Calculation:

Given the expression $2\left[3+7\left(4\right)\right]$ ,

The first step asks to solve the brackets first.

Now as there are two brackets, first solve the small bracket and then big bracket.

Since, $7\left(4\right)$ means $7\times 4$ .

Therefore, the expression finally reduces to

  $2\left[3+7\left(4\right)\right]=2\left[3+7\times 4\right]$

Now, solve the expression inside the big bracket firstly.

That is we first evaluate,

  $3+7\times 4$

Now to evaluate this we again follow order of operations and therefore from step 2 we will first multiply 7 and 4.

  $3+7\times 4=3+28$

Now add 3 and 28, thus we obtain that

  $3+7\times 4=31$

Thus the main expression reduces to

  $2\left[3+7\left(4\right)\right]=2\left[31\right]$

Since, we know that $2\left[31\right]$ means $2\times 31$

Thus,

  $\begin{array}{l}2\left[3+7\left(4\right)\right]=2\left[31\right]\\ =2\times 31\\ =62\end{array}$

Therefore the numerical value of the given expression is 62.

  $2\left[3+7\left(4\right)\right]=62$

Conclusion:

Therefore the numerical value of the given expression is 62.