Question

Estimate each root between two consecutive whole numbers:$\left(a\right)\sqrt{38}\left(b\right)\sqrt[3]{93}$

Short answer

The solution of (a) is $6<\sqrt{38}<7$and (b) is$4<\sqrt[3]{93}<5$

Step-by-step solution

Part (a). Step 1. Given information

The root:$\sqrt{38}$

Part (a) Step 2. Calculation

We have,

$\sqrt{38}$

Number	Square Root
5	25
6	36
7	49
8	64

$36<38<49$

$\sqrt{38}$is between their square rootsrole="math" localid="1645458941171" $6<\sqrt{38}<7$

Part (b) Step 1. Given information

The root:$\sqrt[3]{93}$

Part (b). Step 2. Calculation

We have,

$\sqrt[3]{93}$

Number	Cube Root
3	27
4	64
5	125
6	216

$64<93<125$

$\sqrt[3]{93}$is between their cube rootsrole="math" localid="1645458911884" $4<\sqrt[3]{93}<5$