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High School Mathematics
6.20 Square Roots of Algebraic Expressions Review - II

Square roots of Algebraic Expressions Review Test

Q 1: Find the product of the roots of 2x2 + 7x + 6 = 0.
3
-3
2/5

Q 2: How much is subtracted from 4x4 + 12x3 + 17x2 + 2x + 7 to make it perfect square.
6
5
3
2

Q 3: If one root of 2x2 - (7+a)x - 15 = 0 is 5 find the value of a.
4
3
5
6

Q 4: 3x3 - 6x2y + 3xy2 + 7y3, is this a homogeneous equation?
true
false

Q 5: x3 + y3 + x2 + y2 + x + y, is this symmetry or not.
No
Yes

Q 6: Find the value of a and b so that 9x4 + 6x3 - 17x2 - ax + b is a perfect square.
a = 8 and b = 7
a = 7 and b = 8
a = 6 and b = 9
a = 9 and b = 6

Q 7: Expand, (x + c). (Variables a, b and c)
(x + a) + (x + b) + (x + c)
(x + a)(x + b)(x + c)
(x + a)/(x + b)*(x + c)
(x + a)(x + b)

Q 8: Find the nature of the roots of the equation x2 - 7x + 3 = 0.
Real and equal
Real and distinct
Complex and distinct

Q 9: Find the nature of the roots of the equation 3x2 - 7x + 3 = 0.
Complex and distinct
Real and equal
Real and distinct

Q 10: Solve, 2x4 - 9x3 + 14x2 - 9x + 2 = 0.
1,2 and 1/2
1,1/2 and 2/3
None of these
1,2/3 and 3

Q 11: Find the square root of
(x2 + 10x + 16)(x2 + 11x + 24)(x2 + 5x + 6).
(x + 2)(x + 8)(x + 3)
(x + 2)(x + 8)(x - 3)
(x - 2)(x + 8)(x + 3)
(x + 2)(x - 8)(x + 3)

Q 12: Find the square root of x4 - 4x3 + 8x2 - 8x + 4.
x2 + 2x + 2
x2 - 2x - 2
x2 - 2x + 2
x2 + 2x - 2

Q 13: Solve, 6x4 - x2 - 2 = 0.
(-1/2) and (-2/3)
(1/2) and (2/3)
(-1/2) and (2/3)

Q 14: Find the square root of the equation 4x4 + 8x3 + 9x2 + 4x + 4 = 0 using undetermind method.
2x2 + x + 2
2x2 - x + 2
2x2 + 2x + 2
2x2 + x + 1

Q 15: x3 + 3x2y + xy2 + y3, is this equation symmetry or not?
Yes
No

Q 16: Find the square root of x4 + 6x3 + 15x2 + 18x + 9.
x2 + 3x + 3
x2 - 3x + 3
x + 3x2 + 3

Q 17: Find the square root of (6x2 + 9x - 6)(2x2 + 11x + 12)(3x2 + 10x - 8).
(2x - 3)(3x - 2)(x + 4)
(2x + 3)(3x - 2)(x + 4)
(2x + 3)(3x - 2)(x - 4)
(2x + 3)(3x + 2)(x + 4)

Q 18: What is the first degree expression to be subtracted from 9x4 - 12x3 + 12x2 - 9x + 13.
2x - 4
2x + 4
3x - 4
3x + 4

Q 19: Find the square root of 1296x6y4.
36x4y
36x3y2
36x2y3

Q 20: Solve, 12x4 + 10x2 + 2 = 0
(-1/2) and (--1/3)
(1/2) and (-1/3)
(-1/2) and (-1/3)

Q 21: If one root of 6x2 - (21+a)x + 25 = 0 is 5/2 find the value of a.
7
5
6
4

Q 22: The product of two symmetric expressions is ______.
symmetric
not symmetric

Q 23: Solve, 6x2 + 13x + 5 = 0.
-5/3 and -1/2
-5/3 and 1/2
5/3 and -1/2
5/3 and 1/2

Q 24: Expand, a2b. (Variables 'a' and 'b')
b2a
a2b
a2b + b2a
a2b + ba

Q 25: Find the square root of 16x2y2z4.
4x2yz
4xy2z
4xyz2

Q 26: Find the square root of
(12x2 + 23x + 10)(15x2 + 13x + 2)(20x2 + 29x + 5).
(4x + 3)(3x + 2)(5x + 1)
(4x + 5)(3x + 2)(5x + 1)
(4x + 5)(3x + 2)(5x + 2)
(4x + 5)(3x + 4)(5x + 1)

Q 27: 5x4 - 3x3 + 7x2 - 4x + 2 = 0, is this reciprocal requation or not.
Yes
No

Q 28: Find the quadratic equation whose roots are 9 and 3.
x2 - 6x + 27
x2 - 12x + 27
x2 - 12x - 27
x2 + 12x + 27

Q 29: 3x4 - 5x3 + 3x2 - 4x2 + 5 = 0, is this reciprocal requation or not.
Yes
No

Q 30: How much is subtracted from 16x4 - 24x3 - 23x2 + 24x + 28 to make it perfect square.
16
10
12
8

Q 31: Find the value of a and b so that x4 - 6x3 + 5x2 + ax + b is a perfect square.
a = 8 and b = 7
a = 5 and b = 8
a = 15 and b = 5
a = 12 and b = 4

Q 32: Find the square root of 16x4 - 24x3 - 23x2 + 24x + 16.
4x2 - 3x - 4
4x2 + 3x - 4
4x2 - 3x + 4

Q 33: Find the nature of the roots of the equation 2x2 - 3x + 7 = 0.
Real and equal
Complex and distinct
Real and distinct

Q 34: Solve, 9x4 - 3x2 - 2 = 0.
(-1/3) and (-2/3)
(1/3) and (2/3)
(-1/3) and (2/3)

Q 35: Solve, 8x2 - 14x - 15 = 0.
-3/4 and 5/2
3/4 and 5/2
3/4 and -5/2
-3/4 and -5/2

Q 36: Find the square root of
(x2 + x - 30)(x2 + 8x + 12)(x2 - 3x - 10).
(x - 5)(x + 2)(x - 6)
(x - 5)(x + 2)(x + 6)
(x + 5)(x + 2)(x + 6)
(x - 5)(x - 2)(x + 6)

Q 37: 5x2 + 7y2 + 5z2, is this a homogeneous equation?
true
false

Q 38: Find the product of the roots of 6x2 + 9x - 6 = 0.
1
2
-1

Q 39: Find the square root of
(x2 - 2x - 15)(x2 - 5x - 24)(x2 - 13x + 40).
(x - 8)(x + 5)(x + 3)
(x - 8)(x - 5)(x - 3)
(x - 8)(x - 5)(x + 3)
(x + 8)(x - 5)(x + 3)

Q 40: Find the quadratic equation whose roots are 1/2 and 3/2.
4x2 - 6x + 3
4x2 + 8x + 3
4x2 - 8x - 3
4x2 - 8x + 3

Q 41: Square of the valiable x is _______.
x2
x2

Q 42: Find the square root of the equation x4 + 4x3 + 8x2 + 8x + 4 = 0 using division method.
x2 + 2x + 2
x2 + 2x - 2
x2 + x + 2
x2 + 2x+ 1

Q 43: Solve, 2x2 + 13x + 15 = 0.
-3/2 and -5
3/5 and -5
5/2 and 5
-5/3 and 5

Q 44: Find the quadratic equation whose roots are 6 and 3.
x2 - 9x + 18
x2 + 9x + 18
x2 - 9x - 18
x2 - 9x + 9

Q 45: Find the square root of 25x4 - 20x2y2 + 4y4.
5x2 - 2y2
5x - 2y
5x - 2y2
5x2 - 2y

Q 46: Find the square root of 4x4 + y4 + 9z4 + 4x2y2 - 6y2z2 - 12x2z2.
2x + y + -3z
2x2 + y + 3x2
2x2 + y2 - 3z2

Q 47: If one root of x2 - (7+a)x - 56 = 0 is -8 find the value of a.
-8
8
6
-6

Q 48: Solve, 6x4 - 35x3 + 62x2 - 35x + 6 = 0
2,3,1/2 and 1/3
2,1/2 and 1/3
None of these
3,1/2 and 1/3

Q 49: Find the square root of 9x2 + 24xy + 16y2.
3x + 2y
3x + 4y
2x + 3y

Q 50: 4x22 + xy + 3y2, is this a homogeneous equation?
true
false

Q 51: Find the square root of x2 + 9y2 + 4z2 - 6xy + -12yz + 4xz.
x + 3y + 2z
x + 3y - 2x
x - 3y + 2z

Q 52: Solve, 2x4 - 9x3 + 14x2 - 9x + 2 = 0
1,1/2 and 3/2
1,2 and 1/2
None of these
1,2 and 3/2

Q 53: Find the square root of 625x6.
25x3
25x4
25x2

Q 54: Find the value of ma nd n so that 25x4 + 50x2 + mx + n is a perfect square.
None of these
m = 5 and n = 9
m = 0 and n = 5
m = 0 and n = 25

Q 55: f(x) = 2x2 - 4x + 1, then 3f(x) = _______.
6x2 - 4x + 3
6x2 - 12x + 1
2x2 - 4x + 3
6x2 - 12x + 3

Q 56: Product of two homogeneous expression is a ________.
homogeneous expression
not a homogeneous expression

Q 57: Find the sum of the roots of 6x2 + 13x + 5 = 0.
6/13
-13/6
-6/13
13/6

Q 58: Solve, x2 + 5x + 6 = 0.
-3 and 2
3 and 2
-3 and -2
3 and -2

Q 59: Solve, 6x4 + 11x2 - 3 = 0.
(-3/2) and (-1/3)
(-3/2) and (--1/3)
(3/2) and (-1/3)

Q 60: If one root of x2 - (5+a)x + 24 = 0 is 3 find the value of a.
6
2
5
4

Q 61: What is the first degree expression to be added to x4 + 4x3 - 4x2 - 19x + 11.
3x + 7
2x - 6
3x + 5
2x + 6

Q 62: Find the square root of x2 + 4y2 + 9z2 + 4xy + 6xz + 12yz.
x +2y - 3z
x + 2y + 3z
x - 2y + 3z
None of these

Q 63: What is the first degree expression to be added to x4 + 6x3 + 19x2 + 27x + 23.
2x + 3
2x - 4
3x + 2
2x + 4

Q 64: If one root of 3x2 - (10+a)x + 10 = 0 is 5 find the value of a.
5
6
4
7

Q 65: Find the square root of 961x2y4.
31xy4
31xy2
None of these
31x2y

Q 66: Solve, (x2 - x)2 - 8(x2 - x) + 12 = 0.
-1, -2, 2 and 3
1, -2, 2 and 3
-1, 2, -2 and -3

Q 67: Find the nature of the roots of the equation 4x2 + 5x + 2 = 0.
Complex and distinct
Real and equal
Real and distinct

Q 68: Find the square root of (x - 2y + 3z)2 - 12z(x-2y).
x - 2y - 3z
x - 3y - 3z
x - 2y - 2z

Q 69: Find the sum of roots of the equation 5x2 + 11x + 3 = 0.
12/5
-11/5
-12/5
11/5

Q 70: Find the square root of
(x2 - x - 72)(x2 + x - 56)(x2 - 16x + 63).
(x - 9)(x -7)(x + 8)
(x + 9)(x -7)(x + 8)
(x - 9)(x -7)(x - 8)
(x - 9)(x +7)(x + 8)

Q 71: Find the quadratic equation whose roots are 3/2 and 5/2.
4x2 - 16x + 15
4x2 - 16x + 15
4x2 + 16x + 15
4x2 - 12x + 15

Q 72: Find the square root of 64x2y2.
8xy
8xy2
8x2y
None of these

Q 73: Numbers of the form -6, -5 and -7 are called ________.
imaginary numbers
Real numbers

Q 74: Solve, 2x2 + 7x + 6 = 0.
3/2 and 2
-3/2 and -2
3/2 and -2
-3/2 and 2

Q 75: If all the terms of an algebraic expression are of the same degree, then such an expression is called a _______.
homogeneous expression
not a homogeneous expression

Q 76: Find the sum of the roots of 2x2 + 11x + 12 = 0.
-2/11
-11/2
11/2
2/11

Q 77: Find the square root of 43y4z6.
2xy2z3
2xy3z4
2xyz2
2xy3z3

Q 78: Third degree homogeneous symmetric expression in x and y is _________.
ax3 + bx2y2 + cxy2 + dy3
ax3 + bx2y + cx2y2 + dy3
ax3 + bx2y + cxy2 + dy3
ax2 + bx2y + cxy2 + dy2

Q 79: 5x4 + 6x3y + 3x2y2, is this homogeneous equation?
false
true

Q 80: Solve, 3x2 + x - 10 = 0.
5/3 and -2
-5/3 and 2
-5/3 and -2
5/3 and 2

Q 81: Find the square root of
(6x2 + 16x + 8)(8x2 + 20x + 8)(12x2 + 14x + 4).
(4x + 2)(2x + 4)(4x + 3)
(3x + 2)(x + 4)(4x + 3)
(3x + 2)(2x + 4)(4x + 3)
(3x + 2)(2x + 4)(3x + 3)

Q 82: 3x3 + 4y3 + 5z3. is this a homogeneous equation?
false
true

Q 83: Find the square root of 25x4 + 40x3 - 242 - 32x + 16.
5x2 + 4x + 4
5x2 + 4x - 4
5x2 - 4x + 4

Q 84: Find the square root of 4x4 + 12x3 + 17x2 + 2x + 4.
2x2 - 3x - 2
2x2 - 3x + 2
2x2 + 3x - 2
2x2 + 3x + 2

Q 85: Find the quadratic equation whose roots are 8 and -3.
x2 - 8x - 24
x2 + 5x - 24
x2 - 11x - 24
x2 - 5x - 24

Q 86: Find the square root of 9x4 + 6x2y2 + y4.
3x2 + 2y2
3x2 + y2
3x + y

Q 87: Find the square root of 16x4 + 16x3 + 12x2 + 4x + 1.
4x2 + 2x - 1
4x2 - 2x - 1
4x2 + 2x + 1

Q 88: The quotient of two symmetric expressions is ______.
not symmetric
symmetric

Q 89: Find the square root of x4 - 6x3 + 5x2 + 12x + 4.
x2 + 3x - 2
x2 - 3x + 2
x2 - 3x - 2
x2 + 3x - 2

Q 90: Find the quadratic equation whose roots are 7 and -2.
x2 + 5x - 14
x2 - 5x - 14
x2 - 9x - 14
x2 - 5x + 14

Q 91: If one root of 2x2 - (16+a)x + 25 = 0 is 5/2 find the value of a.
-1
-2
1
2

Q 92: Find the square root of
(x2 + x - 12)(x2 - x - 20)(x2 - 8x + 15).
(x - 5)(x + 3)(x + 4)
(x - 5)(x - 3)(x + 4)
(x + 5)(x - 3)(x + 4)
(x - 5)(x - 3)(x - 4)

Q 93: Find the square root of
(x2 - 4x + 3)(x2 - 12x + 27)(x2 - 10x + 9).
(x - 9)(x - 3)(x - 1)
(x + 9)(x - 3)(x - 1)
(x - 9)(x + 3)(x - 1)
(x - 9)(x - 3)(x + 1)

Q 94: Find the square root of 44 - 4x3 + 12x2 - 16x + 16.
x2 - 2x + 4
x2 + 2x - 4
x2 + 2x + 4

Q 95: x4 + 2x3 - 3x2 + 2x + 1 = 0, is this reciprocal requation or not.
No
Yes

Q 96: Find the square root of x4 + 6x3 + 13x2 + 12x + 4.
x2 + 3x + 2
x2 - 3x - 2
x2 - 3x + 2
x2 + 3x - 2

Q 97: 2x4 - 3x3 + 5x2 - 3x + 2 = 0, is this reciprocal requation or not.
No
Yes

Q 98: Solve, (x2 - 2x)2 - 11(x2 - 2x) + 24 = 0.
-1, 2, -3 and 4
-1, -2, 3 and 4
-1, 2, 3 and 4

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