Question

Learning Task 1 4/625 11. 796 A. Simplify the radical expressions 1. V63 6. V24 2. 48 7. 781 3. 775 8. V128 4. 99 9. 340 5. 92 12. 128 13. 4/243 14. V3000 10. V135 15.

Answer 1

Question:

Simplify the radical expressions

$1.\ \sqrt{63$     $2.\ \sqrt{48$    $3.\ \sqrt{75$      $4.\ \sqrt{99$      $5.\ \sqrt{92$

$6.\ \sqrt[3]{24}$      $7.\ \sqrt[3]{81}$      $8.\ \sqrt{128}$     $9.\sqrt[3]{40}$     $10.\ \sqrt[3]{135}$

Answer:

$\sqrt{63}= 3 \sqrt7$

$\sqrt{48} = 4\sqrt{3}$

$\sqrt{75} = 5\sqrt{3}$

$\sqrt{99} = 3 \sqrt{11$

$\sqrt{92} = 2\sqrt{23$

$\sqrt[3]{24} = 2 \sqrt[3]{3}$

$\sqrt[3]{81} =3\sqrt[3]{3}$

$\sqrt{128} = 8 \sqrt{2}$

$\sqrt[3]{40} = 2 \sqrt[3]{5}$

$\sqrt[3]{135} =3\sqrt[3]{5}$

Step-by-step explanation:

$1.\ \sqrt{63$    

Express 63 as 9 * 7

$\sqrt{63}= \sqrt{9 * 7$

Split:

$\sqrt{63}= \sqrt{9} * \sqrt7$

$\sqrt{63}= 3 * \sqrt7$

$\sqrt{63}= 3 \sqrt7$

$2.\ \sqrt{48$    

Express 48 as 16 * 3

$\sqrt{48} = \sqrt{16*3}$

Split

$\sqrt{48} = \sqrt{16}*\sqrt{3}$

$\sqrt{48} = 4*\sqrt{3}$

$\sqrt{48} = 4\sqrt{3}$

$3.\ \sqrt{75$    

Express 75 as 25 * 3

$\sqrt{75} = \sqrt{25*3}$

Split

$\sqrt{75} = \sqrt{25}*\sqrt{3}$

$\sqrt{75} = 5\sqrt{3}$

$4.\ \sqrt{99$  

Express 99 as 9 * 11

$\sqrt{99} = \sqrt{9} * \sqrt{11}$

Split

$\sqrt{99} = 3 \sqrt{11$

$5.\ \sqrt{92$

Express 92 as 4 * 23

$\sqrt{92} = \sqrt{4} * \sqrt{23$

$\sqrt{92} = 2* \sqrt{23$

$\sqrt{92} = 2\sqrt{23$

$6.\ \sqrt[3]{24}$    

Express 24 as 8 * 3

$\sqrt[3]{24} = \sqrt[3]{8} * \sqrt[3]{3}$

Express 8 as 2^3

$\sqrt[3]{24} = \sqrt[3]{2^3} * \sqrt[3]{3}$

$\sqrt[3]{24} = 2 \sqrt[3]{3}$

$7.\ \sqrt[3]{81}$

Express 81 as 27 * 3

$\sqrt[3]{81} =\sqrt[3]{27}*\sqrt[3]{3}$

Express 27 as 3^3

$\sqrt[3]{81} =\sqrt[3]{3^3}*\sqrt[3]{3}$

$\sqrt[3]{81} =3\sqrt[3]{3}$

$8.\ \sqrt{128}$    

Express 128 as 64 * 2

$\sqrt{128} = \sqrt{64} * \sqrt{2}$

$\sqrt{128} = 8 \sqrt{2}$

$9.\sqrt[3]{40}$

Express 40 as 8 * 5

$\sqrt[3]{40} = \sqrt[3]{8} * \sqrt[3]{5}$

$\sqrt[3]{40} = \sqrt[3]{2^3} * \sqrt[3]{5}$

$\sqrt[3]{40} = 2 \sqrt[3]{5}$

$10.\ \sqrt[3]{135}$

Express 135 as 27 * 5

$\sqrt[3]{135} =\sqrt[3]{27}*\sqrt[3]{5}$

Express 27 as 3^3

$\sqrt[3]{135} =\sqrt[3]{27}*\sqrt[3]{5}$

$\sqrt[3]{135} =3\sqrt[3]{5}$