Razionalizza la seguente frazione: 4 3 32 = \frac{4}{3\sqrt{32}}= 3 3 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> 4 =

2 6 \frac{\sqrt{2}}{6} 6 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

2 3 \frac{\sqrt{2}}{3} 3 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

2 4 \frac{\sqrt{2}}{4} 4 2 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

Quale proprietà è scorretta?

a 1 n ⋅ b 1 m = ( a ⋅ b ) 1 n ⋅ 1 m a^{\frac{1}{n}}\cdot\ b^{\frac{1}{m}}\ =\left(a\ \cdot\ b\right)^{\frac{1}{n}\cdot\frac{1}{m}} a n 1 ⋅ b m 1 = ( a ⋅ b ) n 1 ⋅ m 1

k h a = h k a ^k\sqrt{^h\sqrt{a}}=\ \ ^{hk}\sqrt{a} k h a <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> <path d="M1001,80H400000v40H1013.1s-83.4,268,-264.1,840c-180.7, 572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7s-12,0,-12,0c-1.3,-3.3,-3.7,-11.7, -7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744c-10,12,-21,25,-33,39s-32,39,-32,39 c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30c26.7,-32.7,52,-63,76,-91s52,-60,52,-60 s208,722,208,722c56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5, -658.5c53.7,-170.3,84.5,-266.8,92.5,-289.5c4,-6.7,10,-10,18,-10z M1001 80H400000v40H1013z"> = h k a <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

( a 1 p ) q = a q p \left(a^{\frac{1}{p}}\right)^q\ =a^{\frac{q}{p}} ( a p 1 ) q = a p q

a 1 t : b 1 t = ( a : b ) 1 t a^{\frac{1}{t}}:\ b^{\frac{1}{t}}\ =\left(a:\ b\right)^{\frac{1}{t}} a t 1 : b t 1 = ( a : b ) t 1

75 − 27 + 48 − 300 = \sqrt{75}-\sqrt{27}+\sqrt{48}-\sqrt{300}= 7 5 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 2 7 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 4 8 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> − 3 0 0 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> =

− 6 ⋅ 3 -6\cdot\sqrt{3} − 6 ⋅ 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

− 4 ⋅ 3 -4\cdot\sqrt{3} − 4 ⋅ 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

− 2 ⋅ 3 -2\cdot\sqrt{3} − 2 ⋅ 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

− 8 ⋅ 3 -8\cdot\sqrt{3} − 8 ⋅ 3 <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z">

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Practice Problem

•

Hard

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CCSS

HSN.RN.A.2, 8.EE.A.1, HSA.APR.C.4

Standards-aligned

Adriano Adriano

Used 66+ times

FREE Resource

22 questions

Show all answers

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Qual è il valore di b se:
$^4\sqrt{\sqrt{\sqrt{a}}}=\ ^b\sqrt{a}$

nessuna delle precedenti

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Qual è il valore di b se:
$\left[\left(3^2\right)^{\frac{1}{3}}\right]^{\frac{ }{ }-1\ }=\ ^{\ b}\sqrt{\frac{1}{9}}$

nessuna delle precedenti

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

$\left[\left(5^{\frac{1}{2}}\right)^{\frac{2}{3}}\cdot\left(5^{\frac{3}{2}}\right)^{\frac{1}{3}}\right]^{\frac{2}{5}}-\ 5^{\frac{1}{3}}$ =

$-\sqrt{5}$

$\sqrt{5}$

nessuna delle precedenti

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

$\left[3^{3\ }\cdot3^{\frac{1}{2}}:\ \left(3^2\cdot3^{\frac{1}{3}}\right)\right]^6\ :3^5\ =$

$3^0$

$3^1$

$3^2$

$3^3$

nessuna delle precedenti

$\left(^6\sqrt{4\sqrt{2}^3\sqrt{4}}\cdot^5\sqrt{^3\sqrt{64}}:\ ^5\sqrt{16^3\sqrt{4}}\right)^6\ =$

$^5\sqrt{8}$

$^5\sqrt{4}$

$^5\sqrt{2}$

$1$

nessuna delle precedenti

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

$\left(\sqrt{2}+\sqrt{11}\right)^2-2\sqrt{2}\left(\sqrt{11}+3\sqrt{2}\right)=$

$-\sqrt{2}$

-1

$\sqrt{2}$

$\left(\sqrt{32}+\sqrt{128}\right):\sqrt{2}-\left(\sqrt{8}\cdot\sqrt{2}+2\ +\sqrt{12}\cdot\sqrt{3}\right)\ =$

$\sqrt{2}$

$\sqrt{3}$

$^3\sqrt{2}$

$^3\sqrt{3}$

nessuna delle risposte precedenti

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Radicali

22 questions

Qual è il valore di b se:
$^4\sqrt{\sqrt{\sqrt{a}}}=\ ^b\sqrt{a}$

Qual è il valore di b se:
$\left[\left(3^2\right)^{\frac{1}{3}}\right]^{\frac{ }{ }-1\ }=\ ^{\ b}\sqrt{\frac{1}{9}}$

$\left[\left(5^{\frac{1}{2}}\right)^{\frac{2}{3}}\cdot\left(5^{\frac{3}{2}}\right)^{\frac{1}{3}}\right]^{\frac{2}{5}}-\ 5^{\frac{1}{3}}$ =

$\left[3^{3\ }\cdot3^{\frac{1}{2}}:\ \left(3^2\cdot3^{\frac{1}{3}}\right)\right]^6\ :3^5\ =$

$\left(^6\sqrt{4\sqrt{2}^3\sqrt{4}}\cdot^5\sqrt{^3\sqrt{64}}:\ ^5\sqrt{16^3\sqrt{4}}\right)^6\ =$

$\left(\sqrt{2}+\sqrt{11}\right)^2-2\sqrt{2}\left(\sqrt{11}+3\sqrt{2}\right)=$

$\left(\sqrt{32}+\sqrt{128}\right):\sqrt{2}-\left(\sqrt{8}\cdot\sqrt{2}+2\ +\sqrt{12}\cdot\sqrt{3}\right)\ =$

Razionalizza la seguente frazione:
$\frac{4}{3\sqrt{32}}=$

$\sqrt{32}+6\cdot\ ^3\sqrt{2}\ -\ \ ^3\sqrt{54}-\sqrt{8}=$

$\left(\sqrt{a^2\cdot\sqrt{a^3}}\cdot\sqrt{\frac{1}{a}}\right)^2=$

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Radicali

22 questions

Qual è il valore di b se: 4a= ba^4\sqrt{\sqrt{\sqrt{a}}}=\ ^b\sqrt{a}4a​​​= ba​

Qual è il valore di b se: [(32)13]−1 = b19\left[\left(3^2\right)^{\frac{1}{3}}\right]^{\frac{ }{ }-1\ }=\ ^{\ b}\sqrt{\frac{1}{9}}[(32)31​]​−1 = b91​​

[(512)23⋅(532)13]25− 513\left[\left(5^{\frac{1}{2}}\right)^{\frac{2}{3}}\cdot\left(5^{\frac{3}{2}}\right)^{\frac{1}{3}}\right]^{\frac{2}{5}}-\ 5^{\frac{1}{3}}[(521​)32​⋅(523​)31​]52​− 531​ =

[33 ⋅312: (32⋅313)]6 :35 =\left[3^{3\ }\cdot3^{\frac{1}{2}}:\ \left(3^2\cdot3^{\frac{1}{3}}\right)\right]^6\ :3^5\ =[33 ⋅321​: (32⋅331​)]6 :35 =

(64234⋅5364: 51634)6 =\left(^6\sqrt{4\sqrt{2}^3\sqrt{4}}\cdot^5\sqrt{^3\sqrt{64}}:\ ^5\sqrt{16^3\sqrt{4}}\right)^6\ =(642​34​​⋅5364​​: 51634​​)6 =

(2+11)2−22(11+32)=\left(\sqrt{2}+\sqrt{11}\right)^2-2\sqrt{2}\left(\sqrt{11}+3\sqrt{2}\right)=(2​+11​)2−22​(11​+32​)=

(32+128):2−(8⋅2+2 +12⋅3) =\left(\sqrt{32}+\sqrt{128}\right):\sqrt{2}-\left(\sqrt{8}\cdot\sqrt{2}+2\ +\sqrt{12}\cdot\sqrt{3}\right)\ =(32​+128​):2​−(8​⋅2​+2 +12​⋅3​) =

Razionalizza la seguente frazione: 4332=\frac{4}{3\sqrt{32}}=332​4​=

32+6⋅ 32 − 354−8=\sqrt{32}+6\cdot\ ^3\sqrt{2}\ -\ \ ^3\sqrt{54}-\sqrt{8}=32​+6⋅ 32​ − 354​−8​=

(a2⋅a3⋅1a)2=\left(\sqrt{a^2\cdot\sqrt{a^3}}\cdot\sqrt{\frac{1}{a}}\right)^2=(a2⋅a3​​⋅a1​​)2=

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Qual è il valore di b se:
$^4\sqrt{\sqrt{\sqrt{a}}}=\ ^b\sqrt{a}$

Qual è il valore di b se:
$\left[\left(3^2\right)^{\frac{1}{3}}\right]^{\frac{ }{ }-1\ }=\ ^{\ b}\sqrt{\frac{1}{9}}$

$\left[\left(5^{\frac{1}{2}}\right)^{\frac{2}{3}}\cdot\left(5^{\frac{3}{2}}\right)^{\frac{1}{3}}\right]^{\frac{2}{5}}-\ 5^{\frac{1}{3}}$ =

$\left[3^{3\ }\cdot3^{\frac{1}{2}}:\ \left(3^2\cdot3^{\frac{1}{3}}\right)\right]^6\ :3^5\ =$

$\left(^6\sqrt{4\sqrt{2}^3\sqrt{4}}\cdot^5\sqrt{^3\sqrt{64}}:\ ^5\sqrt{16^3\sqrt{4}}\right)^6\ =$

$\left(\sqrt{2}+\sqrt{11}\right)^2-2\sqrt{2}\left(\sqrt{11}+3\sqrt{2}\right)=$

$\left(\sqrt{32}+\sqrt{128}\right):\sqrt{2}-\left(\sqrt{8}\cdot\sqrt{2}+2\ +\sqrt{12}\cdot\sqrt{3}\right)\ =$

Razionalizza la seguente frazione:
$\frac{4}{3\sqrt{32}}=$

$\sqrt{32}+6\cdot\ ^3\sqrt{2}\ -\ \ ^3\sqrt{54}-\sqrt{8}=$

$\left(\sqrt{a^2\cdot\sqrt{a^3}}\cdot\sqrt{\frac{1}{a}}\right)^2=$