Find the 5^th root of 32

Find the 5^th root of 243.

Find the 5^th root of 100000

Find the 5^th root of \(\frac{1024}{3125}\)

Simplify the following using addition and subtraction properties of surds:
(i) 5\(\sqrt{3}\) + 18\(\sqrt{3}\)-2\(\sqrt{3}\)
(ii) \(4\sqrt [ 3 ]{ 5 } +2\sqrt [ 3 ]{ 5 } -3\sqrt [ 3 ]{ 5 } \)
(iii) 3\(\sqrt{75}\)+5\(\sqrt{48}\)-\(\sqrt{243}\)
(iv) \(5\sqrt [ 3 ]{ 40 } +2\sqrt [ 3 ]{ 625 } -3\sqrt [ 3 ]{ 320 } \)

Simplify the following using multiplication and division properties of surds:
(i) \(\sqrt { 3 } \times \sqrt { 5 } \times \sqrt { 2 } \)
(ii) \(\sqrt { 35 } \div \sqrt { 7 } \)
(iii) \(\sqrt [ 3 ]{ 27 } \times \sqrt [ 3 ]{ 8 } \times \sqrt [ 3 ]{ 125 } \)
(iv) \((7\sqrt { a } -5\sqrt { b } )(7\sqrt { a } +5\sqrt { b } )\)
(v) \(\left[ \sqrt { \frac { 225 }{ 729 } } -\sqrt { \frac { 25 }{ 144 } } \right] \div \sqrt { \frac { 16 }{ 81 } } \)

Arrange surds in descending order:
(i) \(\sqrt [ 3 ]{ 5 } ,\sqrt [ 9 ]{ 4 } ,\sqrt [ 6 ]{ 3 } \)
(ii) \(\sqrt [ 2 ]{ \sqrt [ 3 ]{ 5 } } ,\sqrt [ 2 ]{ \sqrt [ 3 ]{ 5 } } ,\sqrt [ 3 ]{ \sqrt [ 4 ]{ 7 } } ,\sqrt { \sqrt { 3 } } \) 

Can you get a pure surd when you find
(i) the sum of two surds
(ii) the difference of two surds
(iii) the product of two surds
(iv) the quotient of two surds
Justify each answer with an example.