Express the following decimal expression into rational numbers. 0.86

Can you get a rational number when you compute
(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.

Rationalise the denominator and simplify \(\frac { \sqrt { 48 } +\sqrt { 32 } }{ \sqrt { 27 } -\sqrt { 18 } } \) .

Rationalise the denominator and simplify \(\frac { \sqrt { 5 } }{ \sqrt { 6 } +2 } -\frac { \sqrt { 5 } }{ \sqrt { 6 } -2 } \)

Represent the following numbers in scientific notation:
(i) (300000)² \(\times\) (20000)⁴
(ii) (0.000001)¹¹ ÷ (0.005)³
(iii) \( \{ (0.00003 ) ^{ 6 }\times (0.00005)^{ 4 }\} \div \{ (0.009)^{ 3 }\times (0.05)^{ 2 }\} \)

Represent the following information in scientific notation:
(i) The world population is nearly 7000,000,000.
(ii) One light year means the distance 9460528400000000 km.
(iii) Mass of an electron is 0.000 000 000 000 000 000 000 000 000 00091093822 kg.

Can you reduce the following numbers to surds of same order :
(i) \(\sqrt{3}\)
(ii) \(\sqrt [ 4 ]{ 3 } \)
(iii) \(\sqrt [ 3 ]{ 3 } \)

Express each of the following surds in its simplest form \(\sqrt [ 3 ]{ (1024)^{ -2 } } \) and find its order, radicand and coefficient.

(i) Add 3\(\sqrt{7}\) and 5\(\sqrt{7}\) . Check whether the sum is rational or irrational.
(ii) Subtract 4\(\sqrt{5}\) from 7\(\sqrt{5}\) . Is the answer rational or irrational?

Express in scientific notation:
(i) 9768854
(ii) 0.04567891
(iii) 72006865.48