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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: Solve, 6x2 + 7x + 2 = 0.
-1/2 and -2/3
1/2 and 2/3
-1/2 and 2/3
1/2 and -2/3

Q 2: If one root of 3x2 - (10+a)x + 10 = 0 is 5 find the value of a.
7
4
5
6

Q 3: Find the square root of 225x4.
15x2
15x3
15x

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

Q 5: Find the quadratic equation whose roots are 1/2 and 3/2.
4x2 - 8x - 3
4x2 + 8x + 3
4x2 - 8x + 3
4x2 - 6x + 3

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

Q 7: Find the quadratic equation whose roots are 9 and 3.
x2 - 12x + 27
x2 - 6x + 27
x2 - 12x - 27
x2 + 12x + 27

Q 8: Solve, 12x4 + 10x2 + 2 = 0
(-1/2) and (-1/3)
(-1/2) and (--1/3)
(1/2) and (-1/3)

Q 9: Find the square root of 361x4.
19x
19x3
19x2

Q 10: The sum of two symmetric expression is a _______.
not a symmetric expression
symmetric expression

Q 11: Find the value of m and n so that x4 - 6x3 + 5x2 + mx + n is perfect square.
m = 6 and n = 8
m = 12 and n = 4
m = 4 and n = 12
m = 8 and n = 6

Q 12: Find the square root of 961x2y4.
31xy2
31xy4
31x2y
None of these

Q 13: Find the product of roots of the equation 3x2 + 7x + 6 = 0.
5
2
3
6

Q 14: What is the first degree expression to be subtracted from 9x4 - 12x3 + 12x2 - 9x + 13.
3x + 4
3x - 4
2x + 4
2x - 4

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

Q 16: Find the square root of x4 - 6x3 + 5x2 + 12x + 4.
x2 + 3x - 2
x2 + 3x - 2
x2 - 3x - 2
x2 - 3x + 2

Q 17: Find the product of the roots of 8x2 - 14x - 15 = 0.
8/15
15/8
-15/8
-8/15

Q 18: Find the square root of 9x4 + 6x2y2 + y4.
3x2 + 2y2
3x2 + y2
3x + y

Q 19: 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 20: Find the square root of
(12x2 + 23x + 10)(15x2 + 13x + 2)(20x2 + 29x + 5).
(4x + 5)(3x + 2)(5x + 2)
(4x + 5)(3x + 2)(5x + 1)
(4x + 5)(3x + 4)(5x + 1)
(4x + 3)(3x + 2)(5x + 1)

Q 21: Find the square root of (x - 2y + 3z)2 - 12z(x-2y).
x - 3y - 3z
x - 2y - 2z
x - 2y - 3z

Q 22: Find the square root of (x + 2)(x + 4)(x + 6)(x + 8) + 16.
x2 + 8x + 20
x2 + 10x + 15
x2 + 10x + 20

Q 23: Square of the valiable x is _______.
x2
x2

Q 24: Find the square root of the equation 4x4 + 8x3 + 9x2 + 4x + 4 = 0 using undetermind method.
2x2 + x + 1
2x2 - x + 2
2x2 + 2x + 2
2x2 + x + 2

Q 25: 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 26: Find the square root of x2 + 4y2 + 9z2 + 4xy + 6xz + 12yz.
None of these
x + 2y + 3z
x - 2y + 3z
x +2y - 3z

Q 27: Find the square root of 4x4 + 12x3 + 17x2 + 2x + 4.
2x2 + 3x - 2
2x2 + 3x + 2
2x2 - 3x - 2
2x2 - 3x + 2

Q 28: Find the product of the roots of 6x2 - 13x + 6 = 0.
1
5
-1

Q 29: Find the quadratic equation whose roots are 3/4 and 1/2.
8x2 - 10x - 3
8x2 - 10x + 3
8x2 + 10x + 3
8x2 - 8x + 3

Q 30: What is the first degree expression to be subtracted from 16x4 + 16x3 + 20x2 + 10x - 1.
3x + 4
2x - 3
3x - 4
2x - 4

Q 31: 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 32: If one root of 2x2 - (16+a)x + 25 = 0 is 5/2 find the value of a.
-2
-1
2
1

Q 33: The quotient of two symmetric expressions is ______.
symmetric
not symmetric

Q 34: If one root of x2 - (5+a)x + 24 = 0 is 3 find the value of a.
5
2
6
4

Q 35: Find the value of m and n so that x4 - 4x2 + mx + n is a perfect square.
m = 4 and n = 0
m = 0 and n = 4
m = 2 and n = 3
None of these

Q 36: Find the square root of 43y4z6.
2xyz2
2xy3z4
2xy3z3
2xy2z3

Q 37: How much is subtracted from 16x4 - 24x3 - 23x2 + 24x + 28 to make it perfect square.
12
16
8
10

Q 38: Solve, x2 - 11x + 28 = 0.
-4 and 7
4 and 7
4 and -7
-4 and -7

Q 39: 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 40: 3x3 - 6x2y + 3xy2 + 7y3, is this a homogeneous equation?
false
true

Q 41: Solve, 12x2 - x - 1 = 0.
-1/4 and -1/3
-1/4 and 1/3
1/4 and -1/3
1/4 and 1/3

Q 42: Expand, a2b. (Variables 'a' and 'b')
b2a
a2b
(a2b)+(b2a)
(a2b)(b2a)

Q 43: If one root of 2x2 - (7+a)x - 15 = 0 is 5 find the value of a.
4
6
5
3

Q 44: 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 45: 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 46: Find the square root of 16x4 + 16x3 + 12x2 + 4x + 1.
4x2 + 2x - 1
4x2 + 2x + 1
4x2 - 2x - 1

Q 47: Find the value of a and b so that 9x4 + 6x3 - 17x2 - ax + b is a perfect square.
a = 7 and b = 8
a = 6 and b = 9
a = 9 and b = 6
a = 8 and b = 7

Q 48: Find the square root of the equation x4 + 4x3 + 8x2 + 8x + 4 = 0 using division method.
x2 + 2x+ 1
x2 + 2x - 2
x2 + x + 2
x2 + 2x + 2

Q 49: Numbers of the form -6, -5 and -7 are called ________.
imaginary numbers
Real numbers

Q 50: Solve, 6x4 - 35x3 + 62x2 - 35x + 6 = 0
3,1/2 and 1/3
2,3,1/2 and 1/3
None of these
2,1/2 and 1/3

Q 51: Find the square root of 1296x6y4.
36x4y
36x2y3
36x3y2

Q 52: Find the value of ma nd n so that 25x4 + 50x2 + mx + n is a perfect square.
None of these
m = 0 and n = 25
m = 5 and n = 9
m = 0 and n = 5

Q 53: Find the square root of 4x4 - 4x3 - 7x2 + 4x + 4
2x2 - x + 2
2x2 - x - 2
2x2 + x - 2
2x2 + x + 2

Q 54: Find the sum of the roots of 6x2 + 13x + 5 = 0.
-6/13
-13/6
6/13
13/6

Q 55: Simplify, (b-c)(b+c). (Variables a, b and c)
0
3
2
1

Q 56: x4 + 2x3 - 3x2 + 2x + 1 = 0, is this reciprocal requation or not.
No
Yes

Q 57: Find the nature of the roots of the equation x2 - 5x + 6 = 0.
Real and equal
Real and distinct
Complex and distinct

Q 58: Solve, 6x2 + 9x - 6 = 0.
-3/2 and -2/3
3/2 and -2/3
-3/2 and 2/3
3/2 and 2/3

Q 59: Find the square root of 9x4 + 6x3 - 17x2 - 6x + 9.
3x2 - x + 3
3x2 + x - 3
3x2 + x + 3
3x2 - x - 3

Q 60: Find the sum of the roots of 6x2 + 7x + 2 = 0.
-6/7
7/6
-7/6
6/7

Q 61: Solve, 3x2 + x - 10 = 0.
-5/3 and 2
5/3 and -2
-5/3 and -2
5/3 and 2

Q 62: Solve, 6x4 + 11x2 - 3 = 0.
(-3/2) and (-1/3)
(3/2) and (-1/3)
(-3/2) and (--1/3)

Q 63: What is the first degree expression to be added to x4 + 4x3 - 4x2 - 19x + 11.
2x + 6
2x - 6
3x + 5
3x + 7

Q 64: Find the square root of 44 - 4x3 + 12x2 - 16x + 16.
x2 + 2x + 4
x2 - 2x + 4
x2 + 2x - 4

Q 65: Find the nature of the roots of the equation 3x2 - 15x + 5 = 0.
Complex and distinct
Real and distinct
Real and equal

Q 66: Find the square root of 25x4 - 20x2y2 + 4y4.
5x2 - 2y
5x - 2y
5x2 - 2y2
5x - 2y2

Q 67: If one root of x2 - (7+a)x - 56 = 0 is -8 find the value of a.
6
8
-6
-8

Q 68: How much is to be added to 4x4 - 12x3 - 11x2 + 30x + 21 to make it perfect square.
4
7
5
3

Q 69: Find the square root of 64x2y2.
8xy
8x2y
8xy2
None of these

Q 70: Solve, 2x4 - 9x3 + 14x2 - 9x + 2 = 0
1,2 and 3/2
None of these
1,2 and 1/2
1,1/2 and 3/2

Q 71: Solve, 9x4 - 3x2 - 2 = 0.
(-1/3) and (2/3)
(1/3) and (2/3)
(-1/3) and (-2/3)

Q 72: 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 73: Find the quadratic equation whose roots are 8 and -3.
x2 - 8x - 24
x2 + 5x - 24
x2 - 5x - 24
x2 - 11x - 24

Q 74: 3x + 4y + 5, is this a homogeneous equation?
true
false

Q 75: Solve, x2 - x - 20 = 0.
4 and 5
4 and -5
-4 and 5
-4 and -5

Q 76: First degree homogeneous expression in x and y is _____.
ax + by
ac * by

Q 77: If one root of x2 - (4+a)x - 15 = 0 is -3 find the value of a.
-3
2
-2
3

Q 78: Find the quadratic equation whose roots are 7 and -2.
x2 - 9x - 14
x2 - 5x - 14
x2 + 5x - 14
x2 - 5x + 14

Q 79: Find the square root of 16x4 - 24x3 - 23x2 + 24x + 16.
4x2 + 3x - 4
4x2 - 3x + 4
4x2 - 3x - 4

Q 80: Find the square root of 25x2.
15x
None of these
5x2
5x

Q 81: 5x4 - 3x3 + 7x2 - 4x + 2 = 0, is this reciprocal requation or not.
Yes
No

Q 82: 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 83: 3x3 + 5xy2 + 3y3, is this homogeneous equation?
true
false

Q 84: Product of two homogeneous expression is a ________.
homogeneous expression
not a homogeneous expression

Q 85: Find the quadratic equation whose roots are 6 and 3.
x2 - 9x + 18
x2 + 9x + 18
x2 - 18x + 18
x2 - 9x + 9

Q 86: x2 + y2 + z2, is this equation symmetry or not?
No
Yes

Q 87: Find the square root of x4 - 2x3 - 5x2 + 6x + 9.
x2 - x + 3
x2 - x - 3
x2 + x - 3

Q 88: 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 89: Solve, 2x4 - 9x3 + 14x2 - 9x + 2 = 0.
1,1/2 and 2/3
1,2 and 1/2
None of these
1,2/3 and 3

Q 90: Find the value of a and b so that x4 - 6x3 + 5x2 + ax + b is a perfect square.
a = 12 and b = 4
a = 8 and b = 7
a = 15 and b = 5
a = 5 and b = 8

Q 91: Find the square root of 16x2 - 8xy + y2.
4x - y2
4x2 - y
4x - y

Q 92: Find the square root of x4 + 6x3 + 15x2 + 18x + 9.
x2 + 3x + 3
x2 - 3x + 3
x + 3x2 + 3

Q 93: Solve, (2x2 - 3x)2 - 4(2x2 - 3x) - 5 = 0.
-1, 1, -1/2 and 5/2
-1, 1, 1/2 and 5/2
1, 1, 1/2 and 5/2

Q 94: Find the nature of the roots of the equation 3x2 - 7x + 3 = 0.
Real and equal
Complex and distinct
Real and distinct

Q 95: Find the square root of 16x4 - 24x3 - 23x2 + 24x + 16.
4x2 - 3x - 4
4x2 + 3x + 4
4x2 + 3x - 4
4x2 - 3x + 4

Q 96: Find the square root of 4x4 + 16x3 + 24x2 + 16x + 4.
2x2 + 4x + 2
2x2 + 4x - 2
2x2 - 4x + 2
2x2 - 4x - 2

Q 97: Find the sum of the roots of 2x2 + 11x + 12 = 0.
-2/11
2/11
11/2
-11/2

Q 98: Find the square root of x4 + 6x3 + 13x2 + 12x + 4.
x2 - 3x + 2
x2 - 3x - 2
x2 + 3x - 2
x2 + 3x + 2

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