Question

Please solve these questions

Answer 1

(i)
16^1/5 * 2^1/5 = (2^4)^1/5 * 2^1/5 = 2^(4/5) * 2^(1/5) = 2((4+1)/5 = 2

(ii)
243^1/4 / 3^1/4 = (3^5)^1/4 / 3^1/4 = 3^(5-1)/4 = 3

(iii)
(3+root2)*(4+root7) = 12 + 3root7 + 4root2 + root14 = 29.34(approx

(iv)
(root3 - root2)^2 = 3 - 2*root3*root2 + 2 = 5 - 2 root 6 = 0.101(approx.)
Hope it helps.

Answer 2

Solution 1.)

$\sqrt[5]{16} \times \sqrt[5]{2} \\ \\ = {16}^{ \frac{1}{5} } \times {2 }^{ \frac{1}{5} } \\ \\ = {2}^{ \frac{4}{5} } \times {2}^{ \frac{1}{5} } \\ \\ = {2}^{( \frac{4}{5} + \frac{1}{5} )} \\ \\ = {2}^{1} \\ \\ = 2$

Solution 2.)

$\frac{ \sqrt[4]{243} }{ \sqrt[4]{3} } \\ \\ = \sqrt[4]{ \frac{243}{3} } \\ \\ = \sqrt[4]{81} \\ \\ = 3$
Solution 3.)

$(3 + \sqrt{2} )(4 + \sqrt{7} ) \\ \\ = 12 + 4 \sqrt{2} + 3 \sqrt{7} + \sqrt{14}$
Solution 4.)

${( \sqrt{3} - \sqrt{2} )}^{2} \\ \\ = {( \sqrt{3} )}^{2} + ( { \sqrt{2} )}^{2} - 2( \sqrt{3} )( \sqrt{2} ) \\ \\ = 3 + 2 - 2 \sqrt{6} \\ \\ = 5 - 2 \sqrt{6}$