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4 ESO Academics -Unit 02 - Exercises 4.2.2 - Radicals
- 1. UNIT 02 October 1. Find out the value of k in the following radicals: 2. Solve: 3. Solve: 4. Express the following radicals as powers 5. A radical has two roots, if we know one of them, could we know the other one? 6. Two radicals are equivalents, if we know the roots of one of them, could we know the roots of the other one? √𝐤𝐤 𝟑𝟑 = 𝟓𝟓 √−𝟐𝟐𝟐𝟐𝟐𝟐 𝒌𝒌 = −𝟑𝟑 √𝐤𝐤 𝟒𝟒 = 𝟑𝟑 𝟐𝟐 �𝟐𝟐, 𝟎𝟎𝟎𝟎𝟎𝟎 𝒌𝒌 = 𝟐𝟐 √𝟖𝟖𝟖𝟖 𝟒𝟒 = �−𝟏𝟏𝟏𝟏𝟏𝟏, 𝟎𝟎𝟎𝟎𝟎𝟎 𝟓𝟓 = √𝟔𝟔𝟔𝟔𝟔𝟔 𝟒𝟒 = √𝟑𝟑𝟑𝟑 𝟓𝟓 = √−𝟐𝟐𝟐𝟐𝟐𝟐 𝟒𝟒 = �𝟏𝟏, 𝟐𝟐𝟐𝟐𝟐𝟐 𝟒𝟒 = 𝟒𝟒 𝟏𝟏 𝟐𝟐 = 𝟏𝟏𝟏𝟏𝟏𝟏 𝟏𝟏 𝟑𝟑 = 𝟔𝟔𝟔𝟔𝟔𝟔 𝟏𝟏 𝟒𝟒 = 𝟖𝟖 𝟐𝟐 𝟑𝟑 = 𝟔𝟔𝟔𝟔 𝟓𝟓 𝟔𝟔 = 𝟑𝟑𝟑𝟑 𝟑𝟑 𝟐𝟐 = � 𝟑𝟑𝟐𝟐𝟑𝟑 = �(−𝟔𝟔)𝟕𝟕𝟗𝟗 = � 𝟑𝟑𝟐𝟐𝟒𝟒 = � 𝟓𝟓−𝟐𝟐𝟑𝟑 = � 𝟓𝟓𝟐𝟐𝟑𝟑 = � 𝟐𝟐𝟑𝟑𝟔𝟔 = Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.2.2.1
- 2. UNIT 02 October 7. Reduce to same index: 8. Simplify: 9. Extract factors: √𝟐𝟐 𝒂𝒂𝒂𝒂𝒂𝒂 √𝟑𝟑 𝟑𝟑 √𝟑𝟑 𝒂𝒂𝒂𝒂𝒂𝒂 √𝟐𝟐 𝟒𝟒 √𝟓𝟓 𝟑𝟑 𝒂𝒂𝒂𝒂𝒂𝒂 √𝟑𝟑 𝟒𝟒 √𝟕𝟕 𝟑𝟑 𝒂𝒂𝒂𝒂𝒂𝒂 √𝟑𝟑 𝟓𝟓 √𝟏𝟏𝟏𝟏 𝟒𝟒 𝒂𝒂𝒂𝒂𝒂𝒂 √𝟑𝟑 𝟓𝟓 √𝟕𝟕 𝟓𝟓 𝒂𝒂𝒂𝒂𝒂𝒂 √𝟔𝟔 𝟕𝟕 � 𝟓𝟓𝟐𝟐𝟔𝟔 �𝟑𝟑𝟕𝟕𝟐𝟐𝟐𝟐 � 𝟑𝟑𝟒𝟒𝟏𝟏𝟏𝟏 � 𝟕𝟕𝟑𝟑𝟔𝟔 √𝟐𝟐𝟐𝟐 √𝟗𝟗𝟗𝟗 �𝟏𝟏, 𝟔𝟔𝟔𝟔𝟔𝟔 √𝟒𝟒𝟒𝟒 𝟑𝟑 √𝟏𝟏𝟏𝟏𝟏𝟏 𝟑𝟑 �𝟑𝟑, 𝟐𝟐𝟐𝟐𝟐𝟐 𝟑𝟑 √𝟒𝟒𝟒𝟒𝟒𝟒 𝟒𝟒 √𝟏𝟏𝟏𝟏𝟏𝟏 𝟒𝟒 �𝟑𝟑, 𝟖𝟖𝟖𝟖𝟖𝟖 𝟑𝟑 Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.2.2.2
- 3. UNIT 02 October 10. Extract factors: 11. Extract factors: 12. Extract factors: �𝟐𝟐𝟓𝟓 �𝟑𝟑𝟕𝟕 �𝟓𝟓𝟓𝟓 � 𝟕𝟕𝟒𝟒𝟑𝟑 � 𝟏𝟏𝟏𝟏𝟖𝟖𝟑𝟑 � 𝟑𝟑𝟓𝟓𝟑𝟑 � 𝟔𝟔𝟔𝟔𝟒𝟒 � 𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟒𝟒 � 𝟖𝟖𝟕𝟕𝟑𝟑 �𝟐𝟐𝟏𝟏𝟏𝟏 ∙ 𝟓𝟓𝟐𝟐𝟐𝟐 ∙ 𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 � 𝟐𝟐𝟐𝟐𝟐𝟐 ∙ 𝟑𝟑𝟓𝟓𝟓𝟓 ∙ 𝟓𝟓𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 � 𝟑𝟑𝟑𝟑𝟑𝟑 ∙ 𝟏𝟏𝟏𝟏𝟓𝟓𝟓𝟓 ∙ 𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟑𝟑 � 𝟑𝟑𝟓𝟓 ∙ 𝟕𝟕𝟒𝟒 ∙ 𝟏𝟏𝟏𝟏𝟐𝟐𝟐𝟐𝟏𝟏𝟏𝟏 � 𝟐𝟐𝟑𝟑𝟑𝟑 ∙ 𝟏𝟏𝟏𝟏𝟐𝟐 ∙ 𝟐𝟐𝟐𝟐𝟓𝟓𝟑𝟑 � 𝟐𝟐𝟑𝟑𝟑𝟑 ∙ 𝟑𝟑𝟏𝟏𝟏𝟏 ∙ 𝟏𝟏𝟏𝟏𝟒𝟒𝟒𝟒𝟐𝟐𝟐𝟐 � 𝟐𝟐𝟏𝟏𝟏𝟏 ∙ 𝟕𝟕𝟐𝟐𝟐𝟐 ∙ 𝟏𝟏𝟏𝟏𝟓𝟓𝟓𝟓𝟒𝟒 � 𝟐𝟐𝟗𝟗𝟗𝟗 ∙ 𝟓𝟓𝟖𝟖𝟖𝟖 ∙ 𝟕𝟕𝟏𝟏𝟏𝟏𝟒𝟒𝟒𝟒 �𝐱𝐱𝟕𝟕 𝒚𝒚𝟏𝟏𝟏𝟏 𝒛𝒛𝟒𝟒 �𝟏𝟏𝟏𝟏𝟏𝟏𝒙𝒙𝟓𝟓 𝒚𝒚𝟔𝟔 𝒛𝒛𝟕𝟕 �𝐱𝐱𝟏𝟏𝟏𝟏 𝒚𝒚𝒛𝒛𝟑𝟑 �𝟏𝟏𝟏𝟏𝒙𝒙𝟐𝟐𝟐𝟐 𝒚𝒚𝟒𝟒 𝒛𝒛𝟐𝟐𝟑𝟑 �𝐱𝐱𝟏𝟏𝟏𝟏 𝒚𝒚𝟕𝟕 𝒛𝒛𝟓𝟓𝟑𝟑 �𝟑𝟑𝟑𝟑𝒙𝒙𝟏𝟏𝟏𝟏 𝒚𝒚𝟐𝟐𝟐𝟐 𝒛𝒛𝟑𝟑𝟑𝟑𝟒𝟒 � 𝒙𝒙𝟏𝟏𝟏𝟏 𝒚𝒚𝟕𝟕𝟕𝟕 𝒛𝒛𝟐𝟐𝟐𝟐𝟒𝟒 �𝟐𝟐𝟖𝟖𝟖𝟖𝒙𝒙𝟐𝟐 𝒚𝒚𝟏𝟏𝟏𝟏 𝒛𝒛𝟐𝟐𝟐𝟐𝟓𝟓 Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.2.2.3
- 4. UNIT 02 October 13. Solve: 14. Solve: 15. Simplify: 16. Simplify: 𝟔𝟔√𝟑𝟑 + 𝟕𝟕√𝟑𝟑 −√𝟕𝟕 − 𝟑𝟑√𝟕𝟕 𝟓𝟓√𝟏𝟏𝟏𝟏 − 𝟑𝟑√𝟏𝟏𝟏𝟏 𝟐𝟐√𝟕𝟕 + 𝟏𝟏𝟏𝟏 ∙ √ 𝟕𝟕 𝟑𝟑 √𝟓𝟓 − √𝟓𝟓 𝟐𝟐 𝟐𝟐 𝟑𝟑 √𝟐𝟐 − √𝟐𝟐 𝟐𝟐 √𝟒𝟒 ∙ √𝟓𝟓 𝟑𝟑 √𝟔𝟔 𝟑𝟑 ÷ √𝟒𝟒 𝟒𝟒 √𝟗𝟗 ∙ √𝟒𝟒 𝟔𝟔 √𝟓𝟓 ÷ √𝟗𝟗 𝟔𝟔 ���𝟓𝟓𝟐𝟐𝟑𝟑 � 𝟔𝟔 ��� 𝟑𝟑𝟐𝟐𝟐𝟐𝟓𝟓 � 𝟏𝟏 𝟐𝟐 √𝟏𝟏𝟎𝟎 − 𝟗𝟗√𝟏𝟏𝟏𝟏 + 𝟒𝟒√𝟏𝟏𝟏𝟏 𝟏𝟏𝟐𝟐√𝟓𝟓 − 𝟗𝟗√𝟓𝟓 − √𝟓𝟓 √𝟑𝟑 𝟒𝟒 ∙ √𝟗𝟗 𝟔𝟔 ∙ √𝟑𝟑 √𝟖𝟖𝟖𝟖 𝟑𝟑 ÷ √𝟑𝟑 𝟓𝟓 ÷ √𝟐𝟐𝟐𝟐 ��√𝟏𝟏𝟏𝟏 𝟑𝟑 � 𝟒𝟒 ���√𝟏𝟏𝟏𝟏 𝟑𝟑 � 𝟐𝟐 � 𝟓𝟓 Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.2.2.4
- 5. UNIT 02 October 17. Solve: √𝟐𝟐 ∙ �√𝟑𝟑 − √𝟐𝟐� ��√𝟏𝟏𝟏𝟏 𝟗𝟗 � 𝟑𝟑 ∙ √𝟏𝟏𝟏𝟏 √𝟕𝟕 ∙ �√𝟑𝟑 + √𝟓𝟓� ��√𝟏𝟏𝟓𝟓� 𝟑𝟑 ÷ �√𝟓𝟓� 𝟑𝟑𝟔𝟔 √𝟑𝟑 ∙ �𝟑𝟑√𝟐𝟐 + 𝟐𝟐√𝟐𝟐 𝟓𝟓 � √𝟐𝟐 𝟑𝟑 ∙ � √𝟒𝟒𝟒𝟒 𝟑𝟑 √𝟏𝟏𝟏𝟏 𝟔𝟔 + √𝟑𝟑 𝟔𝟔 𝟑𝟑 � −√𝟓𝟓 ∙ �𝟐𝟐√𝟑𝟑 − √𝟑𝟑 𝟑𝟑 � √𝟒𝟒 ÷ � √𝟐𝟐𝟐𝟐 √𝟏𝟏𝟏𝟏 𝟑𝟑 − 𝟐𝟐 𝟑𝟑 √𝟖𝟖𝟖𝟖 𝟔𝟔 � Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.2.2.5
- 6. UNIT 02 October https://www.quia.com/rr/628289.html Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.2.2.6