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.\ √(128)`
`9.\sqrt[3]{40}`
`10.\ \sqrt[3]{135}`

Answer:

`√(63)= 3 \sqrt7`

`√(48) = 4√(3)`

`√(75) = 5√(3)`

`√(99) = 3 \sqrt{11`

`√(92) = 2\sqrt{23`

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

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

`√(128) = 8 √(2)`

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

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

Explanation:

`1.\ \sqrt{63`

Express 63 as 9 * 7

`√(63)= \sqrt{9 * 7`

Split:

`√(63)= √(9) * \sqrt7`

`√(63)= 3 * \sqrt7`

`√(63)= 3 \sqrt7`

`2.\ \sqrt{48`

Express 48 as 16 * 3

`√(48) = √(16*3)`

Split

`√(48) = √(16)*√(3)`

`√(48) = 4*√(3)`

`√(48) = 4√(3)`

`3.\ \sqrt{75`

Express 75 as 25 * 3

`√(75) = √(25*3)`

Split

`√(75) = √(25)*√(3)`

`√(75) = 5√(3)`

`4.\ \sqrt{99`

Express 99 as 9 * 11

`√(99) = √(9) * √(11)`

Split

`√(99) = 3 \sqrt{11`

`5.\ \sqrt{92`

Express 92 as 4 * 23

`√(92) = √(4) * \sqrt{23`

`√(92) = 2* \sqrt{23`

`√(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.\ √(128)`

Express 128 as 64 * 2

`√(128) = √(64) * √(2)`

`√(128) = 8 √(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}`