Simplifying Radicals - Examples & Practice
Read this topicExplanations 3
- Simplifying Radical Expressions Let's learn how to simplify radical expressions. You can remove constants with perfect factors, but variables change a little. You can use expone…
By Alex Federspiel, Amy Feraco, Jonathan Heller, Anusha Rahman
- (Video) Remove Variables from Radical Expressions by mathman1024 This video by mathman1024 covers radical simplification. Summary\large{\text{Summary}}Summary We simplify a powe…
By Alex Federspiel, Amy Feraco, Jonathan Heller, Caroline K, Anusha Rahman
- Simplest Form in Radical Expressions Radicals, like fractions, can be simplified until you have the smallest possible parts. For starters, lets look at a simplified perfect squa…
By Jonathan Heller, Anusha Rahman
Problems 81
- Simplify. 99\\\sqrt{99}99
- Simplify. 6700\\6\sqrt{700}6700
- Simplify 4150x64\sqrt{150x^6}4150x6, if x>0x>0x>0.
- Simplify 25x⋅615x32\sqrt{5x}\cdot 6\sqrt{15x^3}25x⋅615x3, if x>0x>0x>0.
- Simplify. 111\frac{1}{\sqrt{11}}111
- Simplify. 450\sqrt{450}450
- Simplify. 891\sqrt{891}891
- Simplify 80\sqrt{80}80
- Simplify. 72\sqrt{72}72
- Simplify. 192\sqrt{192}192
- Simplify. 250\sqrt{250}250
- Which of the following equals 112x3\sqrt{112x^3}112x3 if x>0x>0x>0?
- Simplify 20a7b6c5d4\sqrt{20a^7b^6c^5d^4}20a7b6c5d4 if a,b,c,d>0a,b,c,d>0a,b,c,d>0.
- Simplify 12x18y4z8\sqrt{12x^{18}y^4z^8}12x18y4z8 if x,y,z>0x,y,z>0x,y,z>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. 8x4y3z83\sqrt[3]{8x^4y^3z^8}38x4y3z8
- Simplify 16x17y3z94\sqrt[4]{16x^{17}y^3z^9}416x17y3z9 if x,y,z>0x,y,z>0x,y,z>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 249a6b122\sqrt{49a^6b^{12}}249a6b12, if a,b>0a,b>0a,b>0.
- Simplify 12x7\sqrt{12x^7}12x7, if x>0x>0x>0.
- Simplify 343x19y13z6\sqrt{343x^{19}y^{13}z^6}343x19y13z6, if x,y,z>0x,y,z>0x,y,z>0.
- Simplify 84x2yz4\sqrt{84x^{2}yz^4}84x2yz4, if x,y,z>0x,y,z>0x,y,z>0.
- Simplify 300x2y12z7\sqrt{300x^{2}y^{12}z^7}300x2y12z7, if x,y,z>0x,y,z>0x,y,z>0.
- Simplify 228x17y19z16\sqrt{228x^{17}y^{19}z^{16}}228x17y19z16, if x,y,z>0x,y,z>0x,y,z>0.
- Simplify 54x10y7z7\sqrt{54x^{10}y^{7}z^{7}}54x10y7z7, if x,y,z>0x,y,z>0x,y,z>0.
- For how many of the positive integers nnn less than 100100100 does the expression xny4x^n y^4xny4 have a square root of the form xaybx^a y^bxayb, for some integers aaa and bbb?
- Simplify 12xy9x2y6z4\sqrt{12xy\sqrt{9x^2y^6z^4}}12xy9x2y6z4, if x,y,z>0x,y,z>0x,y,z>0.
- Simplify x1+1−xx,\sqrt{\frac{x}{1 + \frac{1-x}{x}}},1+x1−xx, where 0<x<10<x<10<x<1.
- Which of the following is already in simplest form?
- Determine which of the following is in simplest radical form.
- Determine which of the following is in simplest radical form.
- Determine which of the following is in simplest radical form.
- If the area of a square yard is 32 ft232 \text{ ft}^232 ft2, what is the length of one side of the yard expressed in simplest radical form? \\Note that the area of a nnn by nnn …
- If the area of a square yard is 75 ft275 \text{ ft}^275 ft2, what is the length of one side of the yard expressed in simplest radical form? \\Note that the area of a nnn by nnn …
- A painting on a square canvas has area 272727 inches2^22. Express the length of one side in simplest radical form. \\Note that the area of a nnn by nnn square equals the square …
- A painting on a square canvas has area 727272 inches2^22. Express the length of one side in simplest radical form. \\Note that the area of a nnn by nnn square equals the square …
- A square coffee table has surface area 454545 inches2^22. Express the length of one side in simplest radical form. \\Note that the area of a nnn by nnn square equals the square …
- Which squares factor into 363636? (Select all that apply.)
- Which squares factor into 400400400? (Select all that apply.)
- What is 323+32\sqrt[3]{32}+\sqrt{32}332+32 is simplest radical form?
- What is 543+54\sqrt[3]{54}+\sqrt{54}354+54 is simplest radical form?
- 8x2=1\sqrt{8x^2}=18x2=1 Solve for xxx, given that x>0x>0x>0.
- Solve for the possible real value(s) of xxx. 25x4=20\sqrt{25x^4}=2025x4=20
- What is the exponent on xxx in the simplified version of the following expression? 2x2⋅π⋅xy⋅10x3⋅8y\sqrt{2x^2\cdot\pi\cdot xy\cdot10x^3\cdot8y}2x2⋅π⋅xy⋅10x3⋅8y Assume x,yx,yx,y…
- What is the exponent on xxx in the simplified version of the following expression? ex10⋅xy3⋅4x5⋅10y\sqrt{ex^{10}\cdot xy^3\cdot4x^5\cdot10y}ex10⋅xy3⋅4x5⋅10y Assume xxx and yyy …
- What is the sum of the exponents on xxx and yyy in the simplified version of the following expression? 3x12⋅y5⋅5x5⋅12xy\sqrt{3x^{12}\cdot y^5\cdot5x^5\cdot12xy}3x12⋅y5⋅5x5⋅12xy…
- What is the sum of the exponents on xxx and yyy in the simplified version of the following expression? y⋅7x15⋅3y2⋅8x−5⋅19x4y15\sqrt{y\cdot 7x^{15}\cdot 3y^2\cdot8x^{-5}\cdot19x^…
- Which of the following expressions is the fully simplified version of the expression 8x3y9\sqrt{8x^3y^9}8x3y9? Assume xxx and yyy are positive.
- Which of the following expressions is the fully simplified version of the expression 18x6y7\sqrt{18x^6y^7}18x6y7? Assume x,yx,yx,y are positive.
- Find the sum of all the exponents in the simplified version of the following expression: a10b9c8a−4b−5c−6\sqrt{ a^{10}b^{9}c^{8}a^{-4}b^{-5}c^{-6}}a10b9c8a−4b−5c−6 Assume a,b,c…
- If the Rubik's Cube pictured above has a volume of 27x327x^327x3, what is the length of one small colored square? Assume xxx is a positive real.
- Lilly is organizing her Lego bricks into neat rows and columns. If she has 121x2y4121x^2y^4121x2y4 bricks and she wants to have equally-sized rows and columns, how many bricks w…
- Michael is shopping for clothes for a vacation he's taking in the summertime. The vacation is 999 days long and he wants to have xxx unique numbers of outfits for each day. If M…
- If he has collected 250y2250y^2250y2 items in total, where yyy is positive, how many bags will be in each row?
- Suppose the volume of a cube equals x3y6z9x^3 y^6 z^9x3y6z9. Find the length of one side, using the formula V=l3V=l^3V=l3 where lll is the length of one side of the cube.
- Which expression is equivalent to x3y4z10\sqrt{x^3 y^4 z^{10}}x3y4z10? Assume x,y,zx,y,zx,y,z are positive.
- Which expression is equivalent to x2y5z14\sqrt{x^2 y^5 z^{14}}x2y5z14? Assume x,y,zx,y,zx,y,z are positive.
- What is the exponent on xxx in the simplified version of the following expression? x2⋅y5⋅z2⋅x5⋅z3⋅y⋅x⋅z5\sqrt{x^2 \cdot y^5\cdot z^2\cdot x^5\cdot z^3\cdot y\cdot x\cdot z^5}x2⋅…
- What is the exponent on yyy in the simplified version of the following expression? x2⋅y5⋅z2⋅x5⋅z3⋅y⋅x⋅z5\sqrt{x^2 \cdot y^5\cdot z^2\cdot x^5\cdot z^3\cdot y\cdot x\cdot z^5}x2⋅…
- What is the exponent on zzz in the simplified version of the following expression? x2⋅y5⋅z2⋅x5⋅z3⋅y⋅x⋅z5\sqrt{x^2 \cdot y^5\cdot z^2\cdot x^5\cdot z^3\cdot y\cdot x\cdot z^5}x2⋅…
- To help understand what's going on when we remove perfect square factors, think about this: x2y=?\sqrt{x^2y} = ?x2y=? (Assume xxx is real and yyy is positive.)
- To help understand what's going on when we remove perfect square factors, think about this: x2y=?\sqrt{x^2y} = ?x2y=? (Assume x>0x>0x>0 and y>0y>0y>0.)
- You and your best friend are building a treehouse! The square base is measured to be 45 ft245\text{ ft}^245 ft2. How long should a side of the treehouse's base be?
- If xxx is negative, then x2=?\sqrt{x^2} = ?x2=?
- If x<0x<0x<0, then 1−x3=?\frac{1}{\sqrt{-x^3}} = ?−x31=?
- Simplify assuming all variables are nonnegative: a2bc\sqrt{a^2bc}a2bc
- Simplify: a2b2c\sqrt{a^2b^2c}a2b2c (Assume a,b,c≥0a,b,c\geq0a,b,c≥0.)
- Simplify: a2b2c2\sqrt{a^2b^2c^2}a2b2c2 (Assume a,b,c≥0a,b,c\geq0a,b,c≥0.)
- Simplify assuming all variables are nonnegative: a3bc5\sqrt{a^3bc^5}a3bc5
- Simplify: a3bc5\sqrt{a^3bc^5}a3bc5 (Assume a,b,c≥0a,b,c\geq0a,b,c≥0.)
- Simplify: abc\sqrt{abc}abc
- What is (x−x2+42)(x+x2+42)(x-\sqrt{x^2+42})(x+\sqrt{x^2+42})(x−x2+42)(x+x2+42)?
- Simplify: 128\sqrt{128}128
- Simplify: 192\sqrt{192}192
- Simplify: 405\sqrt{405}405
- Simplify: 97200\sqrt{97200}97200
- Simplify: 49392\sqrt{49392}49392
- Simplify: 18\sqrt{18}18
- Simplify: 300\sqrt{300}300
- Simplify: 1350\sqrt{1350}1350