Q. 22 - Intermediate Algebra

Question

In the following exercises, estimate each root between two consecutive whole numbers. 

ⓐ $\sqrt{172}$ ⓑ $\sqrt[3]{200 }$

Step-by-Step Solution

Answer

Part (a) 

Part (b) 

Part (a) Step 1. Given information

(a)$\sqrt{172}$

Estimate each root between two consecutive whole numbers.

Step 2. Explanaiton

Think of the perfect square numbers closest to$172$.

 Make a small table of these perfect squares and their squares roots.

$\begin{array}{cc}\text{Numbr}& \text{Square root}\\ \begin{array}{l}169\\ 196\end{array}& \begin{array}{l}13\\ 14\end{array}\end{array}$

Loca between two consecutive perfect squares.

$169<172<196$

$\sqrt{172}$ is between their square roots.

Psrt (b) Step 3. Given information

(b) $\sqrt[3]{200}$

Estimate each root between two consecutive whole numbers.

Step 4. Explanation

Similarly, we locate $200$ between two perfect cube numbers.

$\begin{array}{cc}\text{Number}& \text{Cube root}\\ \begin{array}{l}125\\ 216\end{array}& \begin{array}{l}5\\ 6\end{array}\end{array}$

Locate $200$between two consecutive perfect cubes.

$\Rightarrow 125<200<216$

$\sqrt[3]{200}$ is between their cube roots.

$5<\sqrt[3]{200}<6$