Evaluate
Question:

Evaluate

(i) $\left(1^{3}+2^{3}+3^{3}\right)^{\frac{1}{2}}$

(ii) $\left[5\left(8^{\frac{1}{3}}+27^{\frac{1}{3}}\right)^{3}\right]^{\frac{1}{4}}$

(iii) $\frac{2^{0}+7^{0}}{5^{0}}$

(iv) $\left[(16)^{\frac{1}{2}}\right]^{\frac{1}{2}}$

 

Solution:

(i) $\left(1^{3}+2^{3}+3^{3}\right)^{\frac{1}{2}}$

$\left(1^{3}+2^{3}+3^{3}\right)^{\frac{1}{2}}=(1+8+27)^{\frac{1}{2}}$

$=(36)^{\frac{1}{2}}$

$=\left[(6)^{2}\right]^{\frac{1}{2}}$

$=6$

(ii) $\left[5\left(8^{\frac{1}{3}}+27^{\frac{1}{3}}\right)^{3}\right]^{\frac{1}{4}}$

$\left[5\left(8^{\frac{1}{3}}+27^{\frac{1}{3}}\right)^{3}\right]^{\frac{1}{4}}=\left\{5\left[\left[(2)^{3}\right]^{\frac{1}{3}}+\left[(3)^{3}\right]^{\frac{1}{3}}\right]^{3}\right\}^{\frac{1}{4}}$

$=\left[5(2+3)^{3}\right]^{\frac{1}{4}}$

$=\left[(5)^{4}\right]^{\frac{1}{4}}$

$=5$

(iii) $\frac{2^{0}+7^{0}}{5^{0}}$

$\frac{2^{0}+7^{0}}{5^{0}}=\frac{1+1}{1}$

$=2$

(iv) $\left[(16)^{\frac{1}{2}}\right]^{\frac{1}{2}}$

$\left[(16)^{\frac{1}{2}}\right]^{\frac{1}{2}}=\left\{\left[(4)^{2}\right]^{\frac{1}{2}}\right\}^{\frac{1}{2}}$

$=\left[(4)^{1}\right]^{\frac{1}{2}}$

$=\left[(2)^{2}\right]^{\frac{1}{2}}$

$=2$

 

Administrator

Leave a comment

Please enter comment.
Please enter your name.