Question:
Simplify the radical expressions
[tex]1.\ \sqrt{63[/tex] [tex]2.\ \sqrt{48[/tex] [tex]3.\ \sqrt{75[/tex] [tex]4.\ \sqrt{99[/tex] [tex]5.\ \sqrt{92[/tex]
[tex]6.\ \sqrt[3]{24}[/tex] [tex]7.\ \sqrt[3]{81}[/tex] [tex]8.\ \sqrt{128}[/tex] [tex]9.\sqrt[3]{40}[/tex] [tex]10.\ \sqrt[3]{135}[/tex]
Answer:
[tex]\sqrt{63}= 3 \sqrt7[/tex]
[tex]\sqrt{48} = 4\sqrt{3}[/tex]
[tex]\sqrt{75} = 5\sqrt{3}[/tex]
[tex]\sqrt{99} = 3 \sqrt{11[/tex]
[tex]\sqrt{92} = 2\sqrt{23[/tex]
[tex]\sqrt[3]{24} = 2 \sqrt[3]{3}[/tex]
[tex]\sqrt[3]{81} =3\sqrt[3]{3}[/tex]
[tex]\sqrt{128} = 8 \sqrt{2}[/tex]
[tex]\sqrt[3]{40} = 2 \sqrt[3]{5}[/tex]
[tex]\sqrt[3]{135} =3\sqrt[3]{5}[/tex]
Step-by-step explanation:
[tex]1.\ \sqrt{63[/tex]
Express 63 as 9 * 7
[tex]\sqrt{63}= \sqrt{9 * 7[/tex]
Split:
[tex]\sqrt{63}= \sqrt{9} * \sqrt7[/tex]
[tex]\sqrt{63}= 3 * \sqrt7[/tex]
[tex]\sqrt{63}= 3 \sqrt7[/tex]
[tex]2.\ \sqrt{48[/tex]
Express 48 as 16 * 3
[tex]\sqrt{48} = \sqrt{16*3}[/tex]
Split
[tex]\sqrt{48} = \sqrt{16}*\sqrt{3}[/tex]
[tex]\sqrt{48} = 4*\sqrt{3}[/tex]
[tex]\sqrt{48} = 4\sqrt{3}[/tex]
[tex]3.\ \sqrt{75[/tex]
Express 75 as 25 * 3
[tex]\sqrt{75} = \sqrt{25*3}[/tex]
Split
[tex]\sqrt{75} = \sqrt{25}*\sqrt{3}[/tex]
[tex]\sqrt{75} = 5\sqrt{3}[/tex]
[tex]4.\ \sqrt{99[/tex]
Express 99 as 9 * 11
[tex]\sqrt{99} = \sqrt{9} * \sqrt{11}[/tex]
Split
[tex]\sqrt{99} = 3 \sqrt{11[/tex]
[tex]5.\ \sqrt{92[/tex]
Express 92 as 4 * 23
[tex]\sqrt{92} = \sqrt{4} * \sqrt{23[/tex]
[tex]\sqrt{92} = 2* \sqrt{23[/tex]
[tex]\sqrt{92} = 2\sqrt{23[/tex]
[tex]6.\ \sqrt[3]{24}[/tex]
Express 24 as 8 * 3
[tex]\sqrt[3]{24} = \sqrt[3]{8} * \sqrt[3]{3}[/tex]
Express 8 as 2^3
[tex]\sqrt[3]{24} = \sqrt[3]{2^3} * \sqrt[3]{3}[/tex]
[tex]\sqrt[3]{24} = 2 \sqrt[3]{3}[/tex]
[tex]7.\ \sqrt[3]{81}[/tex]
Express 81 as 27 * 3
[tex]\sqrt[3]{81} =\sqrt[3]{27}*\sqrt[3]{3}[/tex]
Express 27 as 3^3
[tex]\sqrt[3]{81} =\sqrt[3]{3^3}*\sqrt[3]{3}[/tex]
[tex]\sqrt[3]{81} =3\sqrt[3]{3}[/tex]
[tex]8.\ \sqrt{128}[/tex]
Express 128 as 64 * 2
[tex]\sqrt{128} = \sqrt{64} * \sqrt{2}[/tex]
[tex]\sqrt{128} = 8 \sqrt{2}[/tex]
[tex]9.\sqrt[3]{40}[/tex]
Express 40 as 8 * 5
[tex]\sqrt[3]{40} = \sqrt[3]{8} * \sqrt[3]{5}[/tex]
[tex]\sqrt[3]{40} = \sqrt[3]{2^3} * \sqrt[3]{5}[/tex]
[tex]\sqrt[3]{40} = 2 \sqrt[3]{5}[/tex]
[tex]10.\ \sqrt[3]{135}[/tex]
Express 135 as 27 * 5
[tex]\sqrt[3]{135} =\sqrt[3]{27}*\sqrt[3]{5}[/tex]
Express 27 as 3^3
[tex]\sqrt[3]{135} =\sqrt[3]{27}*\sqrt[3]{5}[/tex]
[tex]\sqrt[3]{135} =3\sqrt[3]{5}[/tex]
