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Q. 107

Expert-verified
Intermediate Algebra
Found in: Page 772
Intermediate Algebra

Intermediate Algebra

Book edition OER 2017
Author(s) OPENSTAX
Pages 1346 pages
ISBN 9780998625720

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Short Answer

Use the Quotient Property to simplify square roots.

(a) 32x5y318x3y

(b) 5x6y940x5y33

(c) 5a8b680a3b24

(a) 4xy3

(b) y2x32

(c) aba42

See the step by step solution

Step by Step Solution

Part (a) Step 1. Given information.

Given expression:

32x5y318x3y.

Part (a) Step 2. Write the concept.

For simplifying the radical expression following formula is used:

abn=anbn andanbn=abn

if an and bn are the real number, b0{"x":[[192,192,192,192,192,192,193,194,194,194,195,195,195,197,199,204,210,216,224,234,236,239,242,245,246,246,244,241,237,232,227,221,214,209,206,204],[287,286,285,286,295,312,334,359,372,374,375],[283,285,292,300,315,336,352,363,368],[318,318,318,318,316,312,310,307,306],[427,425,424,420,416,410,407,406,406,408,412,417,424,434,447,456,460,462,463,461,458,453,449,445]],"y":[[27,30,42,51,69,89,104,116,125,130,134,135,136,131,124,116,107,102,97,95,95,97,101,112,119,126,133,137,140,141,141,141,138,135,134,133],[108,108,108,108,108,108,108,107,106,106,106],[131,131,131,131,131,131,131,131,130],[75,78,89,107,131,148,159,172,175],[98,98,98,101,106,114,123,130,137,143,146,146,146,144,139,133,129,125,119,113,107,101,99,99]],"t":[[0,46,68,80,97,117,133,150,167,183,200,215,249,266,283,299,317,329,346,368,379,400,412,434,448,464,484,502,514,530,548,565,582,599,612,625],[977,995,1031,1081,1098,1116,1131,1152,1167,1179,1188],[1390,1412,1432,1444,1462,1480,1497,1511,1530],[1778,1811,1828,1846,1866,1881,1894,1914,1930],[2238,2240,2245,2263,2279,2296,2314,2328,2345,2365,2382,2394,2412,2428,2446,2464,2480,2494,2513,2531,2544,2562,2580,2594]],"version":"2.0.0"}for any integer n2.

Part (a) Step 3. Calculation32x5y318x3y=32.x2.x3.y2.y18x3y=16x2y29=16242xy2=43xy

Part (b) Step 1. Given information.

Given radical expression:

5x6y940x5y33.

Part (b) Step 2. Write the concept.

For simplifying the radical expression following formula is used:

abn=anbn andanbn=abn

if an and bn are the real number, b0{"x":[[191,189,188,185,182,180,179,179,179,178,179,182,189,201,213,229,238,248,255,259,259,259,254,243,231,214,195,183,178,175,175,175],[280,284,300,311,326,334,335],[277,284,299,313,331,345,350,351],[306,305,304,300,296,293,292,292],[414,411,407,401,397,392,390,390,390,392,399,407,418,424,430,433,433,430,427]],"y":[[38,46,55,68,85,95,102,103,104,104,100,94,83,72,67,65,65,69,77,91,96,103,110,115,116,117,115,112,110,109,108,105],[82,82,83,83,83,83,83],[97,98,100,101,101,101,101,101],[61,67,76,95,125,137,147,150],[66,69,73,81,86,93,97,101,105,108,109,109,107,105,99,88,80,69,64]],"t":[[0,59,74,90,109,124,140,157,176,192,225,240,261,276,291,310,325,341,363,387,394,408,427,443,459,474,495,510,523,542,560,576],[1201,1289,1311,1323,1342,1359,1373],[1957,2039,2058,2072,2091,2108,2121,2173],[2436,2491,2505,2522,2544,2557,2573,2592],[2908,2924,2940,2957,2971,2993,3006,3023,3040,3054,3075,3089,3106,3121,3138,3172,3189,3208,3224]],"version":"2.0.0"}for any integer n2.

Part (b) Step 3. Calculation

5x6y940x5y33=5x5.x.y3.y640x5y33=18.x.y63=(y2)3223.x3=y22x3

Part (c) Step 1. Given information.

Given expression:

5a8b680a3b24.

Part (c) Step 2. Write the concept.

radical expression following formula is used:

abn=anbn andanbn=abn

if an and bn are the real number, b0{"x":[[208,208,208,208,208,209,209,209,210,210,210,212,218,219,231,247,250,267,274,277,280,279,278,267,264,232,228,218,217,215,215,215],[299,303,323,334,366,373,387],[318,332,339,372,380,403,407,408],[362,360,359,355,351,349,345,344,344,344,344],[427,425,425,421,417,416,416,416,422,425,440,458,460,463,469,470,470,470,468,466,457,454,443,439,430]],"y":[[73,77,108,113,120,136,146,147,147,148,145,142,129,127,115,108,107,107,113,117,129,137,140,148,148,154,154,154,154,152,149,148],[117,116,116,116,115,115,113],[135,137,137,137,137,136,135,134],[89,95,98,110,128,135,156,161,170,172,175],[97,97,98,102,110,112,124,126,135,138,142,142,142,141,137,136,127,124,111,107,95,93,90,90,90]],"t":[[0,52,101,108,115,138,163,168,187,206,241,247,274,281,304,327,334,359,381,397,421,443,450,473,481,515,521,547,553,574,596,619],[1204,1284,1307,1315,1340,1347,1374],[1722,1757,1765,1789,1797,1819,1838,1859],[2188,2192,2198,2219,2244,2250,2279,2285,2307,2314,2337],[2706,2710,2715,2737,2760,2766,2789,2796,2820,2829,2853,2879,2886,2894,2920,2928,2955,2962,2989,2997,3021,3028,3053,3061,3079]],"version":"2.0.0"}for any integer n2.

Part (c) Step 3. Calculation

5a8b680a3b24=5a5.a3.b4.b280a3b24=1.a5.b4164=12aba4

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