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Radicals – Answers to exercises – pg.7/7

Posted in Answers by Lia on 04/07/2013

Radicals: pg. 1234567

Exercises are on pg. 6

The theory is on pages 1 through 5.

 

1: (5root{3}{6})*(3root {3}{4}) =  15{root{3}{24}} = 15 {root{3}{8*3}} = 15 {root{3}{{2^3}*3}} = 15(root{3}{2^3})*(root{3}{3}) = 

= (15*2){root{3}{3}} = 30{root{3}{3}}

2: root{12}{{a^6}{b^4}{c^3}} =  (root{12}{a^6})*(root{12}{b^4})*(root{12}{c^3}) = {a^{6/12}}{b^{4/12}}{c^{3/12}} = {a^{1/2}}{b^{1/3}}{c^{1/4}}

3: {root{3}{7a^2}}*{root {3}{a{c^2}}} = {root{3}{7{a^{2 + 1}}{c^2}}} =  {root{3}{7 {a^3}{c^2}}} = (root{3}{7})*(root{3}{a^3})*(root{3}{c^2}) =

= (root{3}{7})*a*(root {3}{c^2}) = a{root{3}{7c^2}}

4: 6(root{3}{4{a^2}c})*(root {3}{2ac}) = 6{root{3}{(4{a^2}c)*(2ac)}} = 6{root{3}{8{a^3}{c^2}}} =

= 6(root{3}{2^3})*(root{3}{a^3})*(root{3}{c^2}) = (6*2)a{root{3}{c^2}} = 12a{root{3}{c^2}}

5:  {root{3}{16{a^4}{c^2}}}/{root {3}{2ac}} = {root{3}{{16{a^4}{c^2}}/{2ac}}} = {root{3}{8{a^{4 - 1}}{c^{2 - 1}} = {root{3}{(16/2)*({a^4}/a)*({c^2}/c)}} ={root{3}{(16/2)*({a^4}/a)*({c^2}/c)}} = {root{3}{8{a^{4 - 1}}{c^{2 - 1}}}} = {root{3}{{2^3}{a^3}{c}}} = 2a{root{3}{c}}

6:  {6{root{3}{8 a{c^5}}}}/{2root {3}{4{a^2}{c^2}}} = (6/2)*root{3}{{8 a{c^5}}/{4{a^2}{c^2}}} =  3*{root{3}{2*({a}/{a^2})*({c^5}/{c^2})}} =  3{root{3}{2*{a^{1 - 2}}*{c^{5 - 2} }}} =

= 3{root{3}{2*{a^{-1}}*{c^{3} }}} = 3{root{3}{{2{c^3}}/a}} = 3c{root{3}{2/a}}

7:   (root{3}{7{a^2}c})^4 = {root{3}{{7^4}{a^{2*4}}{c^4}}} = {root{3}{{7^4}{a^8}{c^4}}}

8:  {{}{23}{}}

9:  {{}{23.4}{}}

10: {approx}{28.7}

 

Exercises are on pg. 6

Radicals: pg. 123456, 7

 

 

 

 

 

 

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