PRACTICE QUESTIONS IN SIMPLIFYING RADICALS
Practice questions on simplifying radicals
Simplify the following radicals :
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Questions : 1) √20 2) √121 3) √52 4) √45 5) 3√72 6) 3√40 7) 3√27 8) 4√243 9) 5√288 10) 6√320 |
Answers : 1) 2√5 2) 11 3) 2√13 4) 3√5 5) 23√9 6) 23√5 7) 3 8) 3√3 9) 2√3 10) 2√5 |
Practice questions on exponents and radicals
Simplify the following :
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Questions : 1) 41/2 2) 2251/2 3) 641/3 4) 10001/3 5) 811/4 6) 321/5 7) 8-1/3 8) 163/4 9) 27-2/3 10) (2 1/4)-1/2 11) (3 3/8)-2/3 12) (125)2/3 13) (16)-3/4 14) (-1000)-2/3 15) (3-6)1/3 16) 27-2/3/27-1/3 |
Answers : 1) 2 Solution 2) 15 Solution 3) 4 Solution 4) 10 Solution 5) 3 Solution 6) 2 Solution 7) 1/2 Solution 8) 8 Solution 9) 1/9 Solution 10) 2/3 Solution 11) 4/9 Solution 12) 25 Solution 13) 1/8 Solution 14) 1/100 Solution 15) 1/9 Solution 16) 1/3 Solution |
Practice questions on simplifying radicals with variables and exponents
Simplify the following radicals with variables :
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Questions : 1) √(16u4v3) 2) √(147m3n3) 3) √(75x2y) 4) 6√(72x2) 5) 3√(8x6y3) 6) 3√(54m5n6) 7) 4√(81m4n8) 8) 5√(32p10q15) |
Answers : 1) 4u2v√v 2) 7mn√(3mn) 3) 5x√(3y) 4) 36x√2 5) 2x2y 6) 3mn3√(2m2) 7) 3mn2 8) 2p2q3 |
Practice questions on operations with radicals
Simplify the following radical expression :
1) 7√30 + 2√75 + 5√50 Solution
2) √27 + √105 + √108 + √45 Solution
3) √45 + 3√20 + √80 - 4√40 Solution
4) 3√5 + 2√95 + 3√117 - √78 Solution
5) 3 √32 - 2√8 + √50 Solution
6) 2 √12 - 3√27 - √243 Solution
7) √54 - √2500 - √24 Solution
8) √45 - √25 - √80 Solution
9) 5√95 - 2√50 - 3√180 Solution
10) √5 x √18 Solution
11) ∛7 x ∛8 Solution
12) ∛13 x ∛5 Solution
13) 3√35 ÷ 2√7 Solution
14) 15√54 ÷ 3√6 Solution
15) (48)1/4 ÷ (72)1/8 Solution
16) 4√3, 18√2, -3√3, 15√2 Solution
17) 2∛2, 24∛2, - 4∛2 Solution
Answers :
1) √30 + 5 √3 + 5 √2
2) 4 √3 + √105
3) 9 √5 - 2 √10
4) 3 √5 + 2 √95 + 9 √13 - √78
5) 13 √2
6) -14 √3
7) -√6 -50
8) -√5 - 5
9) 5 √95 - 10 √2 - 18 √5
10) 3 √5
11) 2 ∛14
12) ∛65
13) (3/2)√5
14) 15
15) (32)1/8
16) √3 + 33√2
17) 22 ∛2
Practice questions on rationalizing the denominator with surds
Rationalize the denominator :
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Questions : 1) 12/√6 2) 4√5/√10 3) 5/√7 4) 12/√72 5) 18/√6 6) 1/(3 + √2) 7) (1 - √5)/(3 + √5) 8) 1/(2 + √5) 9) (6 + √5)/(6 - √5) |
Answers : 1) 2√6 Solution 2) 2√2 Solution 3) 5√7/7 Solution 4) √2 Solution 5) 3√6 Solution 6) (3 - √2)/7 Solution 7) 2 - √5 Solution 8) √5 - 2 Solution 9) (41 + 12√5)/31 |
Practice questions on rationalizing the denominator with variables
Rationalize the denominator :
1) 1/√x Solution
2) 1/(x + √y) Solution
3) (√x + y) / (x - √y) Solution
4) (√x + √y)/√x Solution
5) (√x + √y)/(√x - √y) Solution
6) 1/(x + y√3) Solution
7) 3√(2/3a) Solution
8) Simplify : √(12x2) / √(30x) Solution
9) √(100x/11y) Solution
Answers :
1) √x/x
2) (x - √y) / (x2 - y)
3) [x√x + √xy + xy + y√y] / (x2 - y2)
4) [x + √(xy)]/x
5) (x + 2√(xy) + y) / (x - y)
6) (x - y√3) / (x2 + 3y2)
7) 3√(18a2) / 3a
8) √10x / 5
9) 10√(11xy) / 11y
Practice questions on using distributive property with radicals
Expand and simplify the following radicals :
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Questions : 1) √2 (√5+√2) 2) √3 (1-√3) 3) √11 (2√11-1) 4) 2√3 (√3-√5) 5) (1+√2) (2+√2) 6) (√3+2) (√3-1) 7) (√5+2) (√5-3) 8) (2√2+√3) (2√2-√3) 9) (2+√3) (2+√3) 10) (4-√2) (3+√2) 11) (√7-√3) (√7+√3) 12) (4-√2) (3-√2) |
Answers : 1) √10+2 2) √3-3 3) 22-√11 4) 6-2√15 5) 4+3√2 6) 1+√3 7) -1-√5 8) 5 9) 7+4√3 10) 10+√2 11) 4 12) 14-7√2 |
Practice questions on solving for unknown with radicals
Solve for unknown variables :
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Questions : 1) (x+y√2) (2-√2) = 1+√2 2) (2 - 3√2)(x + y√2) = √2 3) (x+y√2) (3+√2) = 1 4) (a+√2) (2-√2) = 4-b√2 5) (a + b√2)2 = 33+20√2 6) (x+y√2) (3-√2) = -4√2 |
Answers : 1) x = 2 and y = 3/2 2) x = -3/7 and y = -1/7 3) x = 3/7 and y = -1/7 4) a = 3 and b = - 1 5) a = 5 and b = 2 6) x = -8/7 and y = -12/7 |
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