Multiplication and Division Properties of Radicals
Read this topicExplanations 4
- Combine the Terms Under One Radical Unlike adding and subtracting radicals, we can multiply two radicals and change the number underneath. Here's the rule: a×b=a×b\sqrt{a} \time…
By Zora Gilbert, Alex Federspiel, Amy Feraco, Jonathan Heller, Caroline K, Anusha Rahman
- Combine terms under one radical Radical division follows the same rule as radical multiplication. Dividing two radicals means we can instead divide the two numbers under one rad…
By Zora Gilbert, Alex Federspiel, Amy Feraco, Jonathan Heller, Caroline K, Anusha Rahman
- (Video) Multiplying and Dividing Radical Terms This video by mathgirl915 shows you how to multiply and divide radical terms. Summary\large{\text{Summary}}Summary When multiplyin…
By Alex Federspiel, Zora Gilbert, Amy Feraco, Jonathan Heller, Caroline K, Anusha Rahman
- Multiplication and Division Properties of Radicals The Multiplication and Division Properties of Radicals can help you simplify expressions! We can have radicals of any integer …
By Caroline K, Jonathan Heller
Problems 67
- Simplify 25x⋅615x32\sqrt{5x}\cdot 6\sqrt{15x^3}25x⋅615x3, if x>0x>0x>0.
- Simplify. 1803\frac{\sqrt{180}}{\sqrt{3}}3180
- Write 81100\sqrt{\frac{81}{100}}10081 in the form a/ba/ba/b where aaa and bbb share no common factors. Write your answer without spaces.
- Write 10036\sqrt{\frac{100}{36}}36100 in the form ab\frac{a}{b}ba where aaa and bbb share no common factors.
- Write 181\sqrt{\frac{1}{81}}811 in the form ab\frac{a}{b}ba where aaa and bbb share no common factors.
- Write 4964\sqrt{\frac{49}{64}}6449 in the form a/ba/ba/b where aaa and bbb share no common factors. Write your answer without spaces.
- Find 576\sqrt{576}576.
- Find 441\sqrt{441}441.
- Find 1089\sqrt{1089}1089.
- Simplify 20a7b6c5d4\sqrt{20a^7b^6c^5d^4}20a7b6c5d4 if a,b,c,d>0a,b,c,d>0a,b,c,d>0.
- Simplify a10b9c8d7e6f5g4h3j2k1l0\sqrt{a^{10}b^9c^8d^7e^6f^5g^4h^3j^2k^1l^0}a10b9c8d7e6f5g4h3j2k1l0 if a,b,c,d,e,f,g,h,j,k,l>0a,b,c,d,e,f,g,h,j,k,l>0a,b,c,d,e,f,g,h,j,k,l>0.
- Simplify 16(2u)5(3v)4\sqrt{16(2u)^5(3v)^4}16(2u)5(3v)4 if u,v>0u,v>0u,v>0.
- Simplify 8x13y6\sqrt{8x^{13}y^6}8x13y6 if x,y>0x,y>0x,y>0.
- Simplify 18×10.\sqrt{18}\times\sqrt{10}.18×10.
- Simplify 8×7.\sqrt{8}\times\sqrt{7}.8×7.
- Simplify 911×53.9\sqrt{11}\times5\sqrt{3}.911×53.
- Simplify 5×430.\sqrt{5}\times4\sqrt{30}.5×430.
- Simplify 5×420.\sqrt{5}\times4\sqrt{20}.5×420.
- Simplify 1410×37.14\sqrt{10}\times3\sqrt{7}.1410×37.
- Simplify 86×55×43.8\sqrt{6}\times5\sqrt{5}\times4\sqrt{3}.86×55×43.
- Simplify 3681.\frac{\sqrt{36}}{\sqrt{81}}.8136.
- Simplify 1215.\frac{\sqrt{12}}{\sqrt{15}}.1512.
- Simplify 10220.\frac{\sqrt{10}}{2\sqrt{20}}.22010.
- Simplify 53.\frac{\sqrt{5}}{\sqrt{3}}.35.
- Simplify 461520.\frac{4\sqrt{6}}{15\sqrt{20}}.152046.
- Simplify 40153075.\frac{40\sqrt{15}}{30\sqrt{75}}.30754015.
- Simplify 1572811 ÷521722.\frac{15\sqrt{7}}{28\sqrt{11}}\ \div\frac{5\sqrt{21}}{7\sqrt{22}}.2811157 ÷722521.
- Evaluate (34)(x)\left(\sqrt{\frac{3}{4}}\right)(x)(43)(x) if x=3x=\sqrt{3}x=3
- Which of the following is equivalent to a2bc\sqrt{\frac{a^2b}{c}}ca2b if a,b,ca,b,ca,b,c are positive?
- Which of the following is equivalent to abc2,\sqrt{\frac{ab}{c^2}},c2ab, if a,b,ca,b,ca,b,c are positive?
- Which of the following equations gives the square root of the area of a circle (A=πr2)(A=\pi {r}^2)(A=πr2), where rrr is the radius?
- If the area of a square equals 323232 cm, what is the length of one side?
- If the area of a square chessboard equals 64x264x^264x2, what is the length of one black or white square? Suppose xxx is positive.
- If the area of the bookshelf above equals 48x248x^248x2, what is the length of one cubbyhole? Assume x>0x>0x>0.
- The cube-shaped watermelon pictured above has a volume of 40 cm340\,\text{cm}^340cm3. Assuming this measure was calculated using the formula V=length×base×heightV = \text{length…
- Simplify 117⋅16611\sqrt7\cdot16\sqrt6117⋅166
- Simplify 018⋅13110\sqrt{18}\cdot13\sqrt{11}018⋅1311
- Simplify 318⋅763\sqrt{18}\cdot7\sqrt6318⋅76
- Calculate the following: 8×252\sqrt{8}\times\frac{\sqrt{25}}{\sqrt{2}}8×225 Simplify first!
- Calculate the following: −32×18-3\sqrt{2}\times\sqrt{18}−32×18
- Calculate the following: 2(53)×4(35)2\sqrt{\left(\frac{5}{3}\right)}\times4\sqrt{\left(\frac{3}{5}\right)}2(35)×4(53)
- Calculate the following: 13×62×213\sqrt{13}\times6\sqrt{2}\times\sqrt{\frac{2}{13}}13×62×132
- Calculate the following: 3×(27+34)\sqrt{3}\times\left(\sqrt{27}+3\sqrt{4}\right)3×(27+34)
- Which of the following is not equal to the rest?
- Pick the odd one out
- A rectangle has dimensions 27×522\sqrt{7}\times5\sqrt{2}27×52. A square has side length of 30\sqrt{30}30. They are measured in the same units. Which shape has a bigger area?
- Calculate: (522)8\left(5^{2\sqrt{2}}\right)^{^{\sqrt{8}}}(522)8
- Calculate: 823×94×2328\sqrt{\frac{2}{3}}\times\sqrt{\frac{9}{4}}\times2\sqrt{\frac{3}{2}}832×49×223
- Calculate: 4+66\frac{\sqrt{4+6}}{\sqrt{6}}64+6
- Which one is bigger: 26(a)\frac{2}{\sqrt{6}}\quad (a)62(a) 63(b)\frac{\sqrt{6}}{3}\quad (b)36(b)
- Calculate: 327+248\frac{\sqrt{3}}{\sqrt{27}}+\frac{\sqrt{2}}{4\sqrt{8}}273+482
- Which is larger? AB4⋅164⋅16\begin{array}{c|c} \text{A}&\text{B}\\ \hline \sqrt{4\cdot16}&\sqrt{4}\cdot\sqrt{16} \end{array}A4⋅16B4⋅16
- If the number on a slice of pie is bigger, that means the slice of pie is also bigger. If you're a greedy eater, which piece of pie would you choose?
- Evaluate: 9322723\frac{9^{\frac{3}{2}}}{27^{\frac{2}{3}}}2732923
- Evaluate: 1111×12144\frac{\sqrt{11}}{11}\times\frac{\sqrt{121}}{\sqrt{44}}1111×44121
- Evaluate: (119)2÷1181\left(\frac{\sqrt{11}}{9}\right)^2\div\frac{11}{81}(911)2÷8111
- Calculate: 522÷12512\frac{\sqrt{5}}{2\sqrt{2}}\div\frac{\sqrt{125}}{\sqrt{12}}225÷12125
- Which is larger? AB16÷416÷4\begin{array}{c|c} \text{A}&\text{B}\\ \hline \sqrt{16\div4}&\sqrt{16}\div\sqrt{4} \end{array}A16÷4B16÷4
- Which of these expressions is equivalent to: ab\sqrt{\frac{a}{b}}ba if a,b>0a,b>0a,b>0?
- Which of these expressions is equivalent to: ab\sqrt{ab}ab if a,b≥0a,b\geq0a,b≥0?
- Which of these expressions is equivalent to: a2b2\sqrt{\frac{a^2}{b^2}}b2a2 if a,b>0a,b>0a,b>0?
- Which of these expressions is equivalent to: a2b2\sqrt{a^2b^2}a2b2 if a,b≥0a,b\geq0a,b≥0?
- What is 2×2\sqrt2\times\sqrt22×2?
- What is 23×472\sqrt3\times4\sqrt723×47?
- Write 81144\sqrt{\frac{81}{144}}14481 in the form of ab\frac{a}{b}ba where aaa and bbb have no common factors.
- Simplify: 12108\frac{\sqrt{12}}{\sqrt{108}}10812
- Simplify: 1473\frac{\sqrt{147}}{\sqrt{3}}3147