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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 square root of 4x4 + 8x3 + 9x2 + 4x + 4.
2x2 - x + 2
2x2 + x - 2
2x2 + x + 2

Q 2: 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 3: Find the nature of the roots of the equation 3x2 - 12x + 7 = 0.
Complex and distinct
Real and distinct
Real and equal

Q 4: x4 + 2x3 - 3x2 + 2x + 1 = 0, is this reciprocal requation or not.
Yes
No

Q 5: Find the nature of the roots of the equation 3x2 - 7x + 3 = 0.
Real and equal
Real and distinct
Complex and distinct

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

Q 7: Square of the valiable x is _______.
x2
x2

Q 8: Find the nature of the roots of the equation 2x2 - 3x + 7 = 0.
Real and equal
Complex and distinct
Real and distinct

Q 9: Solve, x2 - 4x - 21 = 0.
-3 and -7
3 and -7
3 and 7
-3 and 7

Q 10: Find the product of the roots of 8x2 - 14x - 15 = 0.
8/15
-15/8
-8/15
15/8

Q 11: Find the square root of 16x2 - 8xy + y2.
4x2 - y
4x - y
4x - y2

Q 12: What is the first degree expression to be subtracted from 16x4 + 16x3 + 20x2 + 10x - 1.
3x - 4
3x + 4
2x - 3
2x - 4

Q 13: 5x + 3y+ 15y2, is this a homogeneous equation?
true
false

Q 14: Find the nature of the roots of the equation 4x2 + 5x + 2 = 0.
Real and distinct
Real and equal
Complex and distinct

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

Q 16: 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 + 2)
(4x + 5)(3x + 4)(5x + 1)
(4x + 5)(3x + 2)(5x + 1)

Q 17: Solve, 2x4 - 9x3 + 14x2 - 9x + 2 = 0
1,2 and 3/2
1,2 and 1/2
None of these
1,1/2 and 3/2

Q 18: Find the square root of x4 + y4 + 9z4 - 2x2y2 - 6x2z2 + 6y2z2.
x2 - y2 + 3z2
x2 + y2 + 3z2
x2 - y2 - 3z2

Q 19: Expand, a2b. (Variables 'a' and 'b')
a2b
(a2b)(b2a)
(a2b)+(b2a)
b2a

Q 20: Find the square root of 16x4 + 16x3 + 12x2 + 4x + 1.
4x2 + 2x - 1
4x2 + 2x + 1
4x2 - 2x - 1

Q 21: 5x4 + 6x3y + 3x2y2, is this homogeneous equation?
false
true

Q 22: If one root of x2 - (5+a)x + 24 = 0 is 3 find the value of a.
6
4
5
2

Q 23: If one root of x2 - (7+a)x - 56 = 0 is -8 find the value of a.
8
6
-6
-8

Q 24: 3x4 - 5x3 + 3x2 - 4x2 + 5 = 0, is this reciprocal requation or not.
No
Yes

Q 25: Find the square root of 1296x6y4.
36x3y2
36x4y
36x2y3

Q 26: Find the product of roots of the equation 3x2 + 7x + 6 = 0.
2
3
6
5

Q 27: x2 + y2 + z2, is this equation symmetry or not?
No
Yes

Q 28: 3x3 + 4y3 + 5z3. is this a homogeneous equation?
false
true

Q 29: The difference of two symmetric expression is a ___________.
symmetric expression
not a symmetric expression

Q 30: Find the square root of 43y4z6.
2xy3z4
2xy3z3
2xy2z3
2xyz2

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

Q 33: Find the square root of 9x2 + 24xy + 16y2.
3x + 4y
2x + 3y
3x + 2y

Q 34: Solve, x2 + 5x + 6 = 0.
-3 and 2
-3 and -2
3 and -2
3 and 2

Q 35: Find the square root of 4x4 - 4x3 - 7x2 + 4x + 4
2x2 + x - 2
2x2 - x - 2
2x2 - x + 2
2x2 + x + 2

Q 36: If one root of x2 - (4+a)x - 15 = 0 is -3 find the value of a.
3
-3
2
-2

Q 37: 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 38: Find the square root of x4 - 2x3 - 5x2 + 6x + 9.
x2 - x - 3
x2 + x - 3
x2 - x + 3

Q 39: Solve, 15x4 + 13x2 + 2 = 0.
(2/3) and (-1/5)
(-2/3) and (1/5)
(-2/3) and (-1/5)

Q 40: Find the quadratic equation whose roots are 8 and -3.
x2 + 5x - 24
x2 - 11x - 24
x2 - 8x - 24
x2 - 5x - 24

Q 41: 3x3 - 6x2y + 3xy2 + 7y3, is this a homogeneous equation?
true
false

Q 42: Find the square root of 225x4.
15x2
15x3
15x

Q 43: Find the value of a and b so that 4x4 + 12x3 + 17x2 + ax + b is a perfect square.
a = 2 and b = 4
a = 3 and b = 4
a = 3 and b = 5
a = 4 and b = 5

Q 44: 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 45: Find the quadratic equation whose roots are 3/2 and 5/2.
4x2 - 16x + 15
4x2 - 16x + 15
4x2 - 12x + 15
4x2 + 16x + 15

Q 46: f(x) = 2x2 - 4x + 1, then 3f(x) = _______.
6x2 - 12x + 3
2x2 - 4x + 3
6x2 - 12x + 1
6x2 - 4x + 3

Q 47: Find the quadratic equation whose roots are 7 and -2.
x2 - 9x - 14
x2 - 5x - 14
x2 + 5x - 14
x2 - 5x + 14

Q 48: Solve, 3x2 - 4x - 6 = 0.
2/3 and 3
-2/3 and -3
2/3 and -3
-2/3 and 3

Q 49: Find the square root of 44 - 4x3 + 12x2 - 16x + 16.
x2 + 2x + 4
x2 - 2x + 4
x2 + 2x - 4

Q 50: If all the terms of an algebraic expression are of the same degree, then such an expression is called a _______.
not a homogeneous expression
homogeneous expression

Q 51: Find the square root of x4 - 4x3 + 8x2 - 8x + 4.
x2 - 2x - 2
x2 + 2x - 2
x2 + 2x + 2
x2 - 2x + 2

Q 52: 3x3 + 5xy2 + 3y3, is this homogeneous equation?
false
true

Q 53: 5x4 - 3x3 + 7x2 - 4x + 2 = 0, is this reciprocal requation or not.
Yes
No

Q 54: If one root of 2x2 - (3+a)x + 6 = 0 is 2 find the value of a.
3
4
5
6

Q 55: What is the first degree expression to be subtracted from 4x4 + 8x3 - 8x2 - 9x + 11.
2x - 4
2x + 3
3x + 2
2x + 4

Q 56: x3 + y3 + x2 + y2 + x + y, is this equation symmetry or not?
No
Yes

Q 57: Solve, 6x4 - x2 - 2 = 0.
(-1/2) and (2/3)
(-1/2) and (-2/3)
(1/2) and (2/3)

Q 58: Find the nature of the roots of the equation 3x2 - 15x + 5 = 0.
Real and equal
Complex and distinct
Real and distinct

Q 59: What is the first degree expression to be subtracted from 9x4 - 12x3 + 12x2 - 9x + 13.
2x - 4
2x + 4
3x + 4
3x - 4

Q 60: What is the first degree expression to be added to x4 + 6x3 + 19x2 + 27x + 23.
2x + 3
3x + 2
2x - 4
2x + 4

Q 61: x3 + 3x2y + xy2 + y3, is this equation symmetry or not?
No
Yes

Q 62: Find the sum of the roots of 2x2 + 11x + 12 = 0.
-11/2
2/11
11/2
-2/11

Q 63: Find the square root of 25x2.
5x2
5x
15x
None of these

Q 64: Third degree homogeneous symmetric expression in x and y is _________.
ax3 + bx2y2 + cxy2 + dy3
ax2 + bx2y + cxy2 + dy2
ax3 + bx2y + cxy2 + dy3
ax3 + bx2y + cx2y2 + dy3

Q 65: 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 66: Solve, 6x4 + 11x2 - 3 = 0.
(-3/2) and (-1/3)
(3/2) and (-1/3)
(-3/2) and (--1/3)

Q 67: Solve, 2x2 + 11x + 12 = 0.
3/2 and 4
3/2 and -4
-3/2 and 4
-3/2 and -4

Q 68: 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 69: Find the square root of 64x2y2.
None of these
8x2y
8xy2
8xy

Q 70: The product of two symmetric expressions is ______.
symmetric
not symmetric

Q 71: Find the nature of the roots of the equation 3x2 + 7x - 4 = 0.
Real and equal
Real and distinct
Complex and distinct

Q 72: If one root of 6x2 - (21+a)x + 25 = 0 is 5/2 find the value of a.
5
6
4
7

Q 73: Find the square root of
(6x2 + 16x + 8)(8x2 + 20x + 8)(12x2 + 14x + 4).
(3x + 2)(2x + 4)(3x + 3)
(4x + 2)(2x + 4)(4x + 3)
(3x + 2)(2x + 4)(4x + 3)
(3x + 2)(x + 4)(4x + 3)

Q 74: Find the square root of x2 + 9y2 + 4z2 - 6xy + -12yz + 4xz.
x - 3y + 2z
x + 3y + 2z
x + 3y - 2x

Q 75: 2x4 - 3x3 + 5x2 - 3x + 2 = 0, is this reciprocal requation or not.
Yes
No

Q 76: Solve, (x2 - 2x)2 - 11(x2 - 2x) + 24 = 0.
-1, -2, 3 and 4
-1, 2, -3 and 4
-1, 2, 3 and 4

Q 77: The sum of two symmetric expression is a _______.
not a symmetric expression
symmetric expression

Q 78: 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 79: 5x2 + 7y2 + 5z2, is this a homogeneous equation?
true
false

Q 80: Solve, 9x4 - 3x2 - 2 = 0.
(1/3) and (2/3)
(-1/3) and (-2/3)
(-1/3) and (2/3)

Q 81: The quotient of two symmetric expressions is ______.
not symmetric
symmetric

Q 82: Find the square root of 9x4 + 6x2y2 + y4.
3x2 + y2
3x2 + 2y2
3x + y

Q 83: Find the quadratic equation whose roots are 6 and 3.
x2 + 9x + 18
x2 - 9x + 18
x2 - 9x + 9
x2 - 9x - 18

Q 84: 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 85: If one root of 3x2 - (10+a)x + 10 = 0 is 5 find the value of a.
6
4
5
7

Q 86: How much is subtracted from 4x4 + 12x3 + 17x2 + 2x + 7 to make it perfect square.
6
2
3
5

Q 87: Find the square root of x4 - 6x3 + 5x2 + 12x + 4.
x2 - 3x + 2
x2 + 3x - 2
x2 + 3x - 2
x2 - 3x - 2

Q 88: Find the product of the roots of 6x2 - 13x + 6 = 0.
5
-1
1

Q 89: Find the square root of (x - 2y + 3z)2 - 12z(x-2y).
x - 2y - 2z
x - 2y - 3z
x - 3y - 3z

Q 90: Find the sum of the roots of 6x2 + 7x + 2 = 0.
7/6
6/7
-7/6
-6/7

Q 91: Find the square root of the equation 4x4 + 8x3 + 9x2 + 4x + 4 = 0 using undetermind method.
2x2 + x + 1
2x2 + 2x + 2
2x2 - x + 2
2x2 + x + 2

Q 92: Find the square root of 961x2y4.
31x2y
None of these
31xy4
31xy2

Q 93: Find the product of the roots of 2x2 + 7x + 6 = 0.
2/5
-3
3

Q 94: Find the product of the roots of 6x2 + 9x - 6 = 0.
2
-1
1

Q 95: Solve, x2 - x - 6 = 0.
-3 and -2
-3 and 2
3 and -2
3 and 2

Q 96: Find the square root of x2 + 4y2 + 9z2 + 4xy + 6xz + 12yz.
x - 2y + 3z
x +2y - 3z
x + 2y + 3z
None of these

Q 97: Find the square root of 16x4 - 24x3 - 23x2 + 24x + 16.
4x2 - 3x + 4
4x2 - 3x - 4
4x2 + 3x + 4
4x2 + 3x - 4

Q 98: Solve, 3x4 - 16x3 + 26x2 - 16x + 3 = 0.
1,1/2 and 2/3
1,1/2 and 1/3
1,3 and 2/3
1,3 and 1/3

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Question 100: This question is available to subscribers only!


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