Question

Making use of the cube root table, find the cube root
1346.

Answer 1

By prime factorisation, we have:

$$1346=2\times 673\Rightarrow \sqrt[3]{1346}=\sqrt[3]{2}\times \sqrt[3]{673}$$

Also

$$670<673<680\Rightarrow \sqrt[3]{670}<\sqrt[3]{673}<\sqrt[3]{680}$$

From the cube root table, we have:

$$\sqrt[3]{670}=8.750\text{ and }\sqrt[3]{680}=8.794$$

For the difference (680 - 670), i.e., 10, the difference in the values

$$=8.794-8.750=0.044$$

∴  For the difference of (673 - 670), i.e., 3, the difference in the values 

$$=\frac{0.044}{10}\times 3=0.0132=0.013$$  (upto three decimal places)

∴ $$\sqrt[3]{673}=8.750+0.013=8.763$$

Now $$\sqrt[3]{1346}=\sqrt[3]{2}\times \sqrt[3]{673}=1.260\times 8.763=11.041$$ (upto three decimal places)

Thus, the answer is 11.041.