Q. 21 - Intermediate Algebra

Question

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

ⓐ  $\sqrt{200}$ⓑ $\sqrt[3]{137}$

Step-by-Step Solution

Answer

Part(a)$\sqrt{200}=14<\sqrt{200}<15$

Part(b)

Part (a) Step 1. Given informaiton

(a)$\sqrt{200}$

Estimate each root between two consecutive whole numbers. 

Step 2. Explanaion

Think of the perfect square numbers closest to$200$.

 Make a small table of these perfect squares and their squares roots.$\begin{array}{cc}\text{Numbr}& \text{Square root}\\ \begin{array}{l}196\\ 225\end{array}& \begin{array}{l}14\\ 15\end{array}\end{array}$

Locate$200$ between two consecutive perfect squares.

$196<200<225$

$\sqrt{200}$ is between their square roots.  $14<\sqrt{200}<15$

Part (b) step 3. Given information

(b)$\sqrt[3]{137}$

Estimate each root between two consecutive whole numbers. 

Step 4. Explanation

Similarly, we locate $137$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 $137$between two consecutive perfect cubes.

$\Rightarrow 125<137<216$

$\sqrt[3]{137}$ is between their cube roots.

$5<\sqrt[3]{137}<6$