Question

3root root 0.000729 + root 3 0.008

Answer 1

Given : $\sqrt[3]{0.000729}+\sqrt[3]{0.008}$

To find : simplified value

Solution :

• Here $0.000729 = \frac{729}{1000000}$

• and $0.008 = \frac{8}{1000}$

• $1000000 = 100* 100* 100 = 100^{3}$

• and $1000=10*10*10=10^{3}$

• Now $729=9*9*9=9^{3}$

• and $8=2*2*2=2^{3}$

• So $\frac{729}{1000000}=\frac{9^{3}}{100^{3}}=(\frac{9}{100})^{3}$

• and $\frac{8}{1000}=\frac{2^{3}}{10^{3}}=(\frac{2}{10})^{3}$

• Thus $\sqrt[3]{0.000729}+\sqrt[3]{0.008}$

• $=\sqrt[3]{\frac{729}{1000000}}+\sqrt[3]{\frac{8}{1000}}$

• $=\sqrt[3]{(\frac{9}{100})^{3}}+\sqrt[3]{\frac{2}{10})^{3}}$

• $=\frac{9}{100}+\frac{2}{10}$ since $\sqrt[3]{a^{3}}=a$

• $=0.09+0.2$

• $=0.29$

Answer : $\sqrt[3]{0.000729}+\sqrt[3]{0.008}=0.29$