Square Identity MCQ Quiz - Objective Question with Answer for Square Identity - Download Free PDF
Last updated on Apr 4, 2025
Latest Square Identity MCQ Objective Questions
Square Identity Question 1:
Simplify : \(\rm \frac{0.728 \times 0.728-0.272 \times 0.272}{0.456}\)
Answer (Detailed Solution Below)
Square Identity Question 1 Detailed Solution
Given:
Simplify: (0.728 × 0.728 - 0.272 × 0.272) / 0.456
Formula used:
(a2 - b2) = (a + b)(a - b)
Calculation:
(0.728 × 0.728 - 0.272 × 0.272) / 0.456
⇒ (0.7282 - 0.2722) / 0.456
⇒ ((0.728 + 0.272) × (0.728 - 0.272)) / 0.456
⇒ (1.0 × 0.456) / 0.456
⇒ 0.456 / 0.456
⇒ 1
∴ The correct answer is option (2).
Square Identity Question 2:
The value of [(.253*.253-.253*.067+.067*.067)/(.253*.253*.253+.067*.067*.067)] is:
Answer (Detailed Solution Below)
Square Identity Question 2 Detailed Solution
Given:
\(\dfrac{(.253 \times .253 - .253 \times .067 + .067 \times .067)}{(.253 \times .253 \times .253 + .067 \times .067 \times .067)}\)
Formula used:
\(\dfrac{a^2 - ab + b^2}{a^3 + b^3}\) = \(\dfrac{{a^2 - ab + b^2}}{(a + b)(a^2 - ab + b^2)}\) = \(\dfrac{1}{a + b}\)
Calculation:
Let a = 0.253 and b = 0.067
⇒ \(\dfrac{{(0.253^2 - 0.253 \times 0.067 + 0.067^2)}}{(0.253 + 0.067)(0.253^2 - 0.253 \times 0.067 + 0.067^2)}\)
⇒ \(\dfrac{1}{0.253 + 0.067}\) = (1 / 0.32)
⇒ \(\)3.125
∴ The value of the given expression is 3.125.
Square Identity Question 3:
If a + b = 12 and 4ab = 140, then what is the value of a2 + b2?
Answer (Detailed Solution Below)
Square Identity Question 3 Detailed Solution
Given:
If a + b = 12 and 4ab = 140
Formula used:
(a + b)2 = a2 + b2 + 2ab
Calculation:
(a + b)2 = 122
⇒ 144 = a2 + b2 + 2ab
Since, 4ab = 140
⇒ ab = 35
⇒ 144 = a2 + b2 + 2 × 35
⇒ 144 = a2 + b2 + 70
⇒ a2 + b2 = 74
∴ The correct answer is option 2.
Square Identity Question 4:
Simplify (5z - 7y)2 + (7z + 5y)2 - 49z2
Answer (Detailed Solution Below)
Square Identity Question 4 Detailed Solution
Given:
Simplify (5z - 7y)2 + (7z + 5y)2 - 49z2
Formula used:
(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 - 2ab + b2
Calculation:
(5z - 7y)2 + (7z + 5y)2 - 49z2
⇒ (25z2 - 2 × 5z × 7y + 49y2) + (49z2 + 2 × 7z × 5y + 25y2) - 49z2
⇒ 25z2 - 70zy + 49y2 + 49z2 + 70zy + 25y2 - 49z2
⇒ 25z2 + 49z2 - 49z2 + 49y2 + 25y2
⇒ 25z2 + 74y2
∴ The correct answer is option (4).
Square Identity Question 5:
If x = 4 + √6 and y = 4 - √6 then the value of x2 + y2 is:
Answer (Detailed Solution Below)
Square Identity Question 5 Detailed Solution
Given:
If x = 4 + √6 and y = 4 - √6
Formula used:
x2 + y2 = (x + y)2 - 2xy
Calculation:
x = 4 + √6 and y = 4 - √6
x + y = (4 + √6) + (4 - √6) = 8
x × y = (4 + √6)(4 - √6) = 42 - (√6)2 = 16 - 6 = 10
⇒ x2 + y2 = (8)2 - 2 × 10
⇒ x2 + y2 = 64 - 20
⇒ x2 + y2 = 44
∴ The correct answer is option (3).
Top Square Identity MCQ Objective Questions
Simplify: \(\sqrt {36{x^2} - 108x + 81} \).
Answer (Detailed Solution Below)
Square Identity Question 6 Detailed Solution
Download Solution PDFCalculations:
√(36x² - 108x + 81)
=√[(6x)² - 2 × 6 × 9x + (9)²]
= √[6x - 9]²
= 6x - 9
Hence, The Required value is 6x - 9.
If a + b = 5 and ab = 6, then find 3(a2 + b2).
Answer (Detailed Solution Below)
Square Identity Question 7 Detailed Solution
Download Solution PDFGiven:
a + b = 5 and ab = 6
Concept used:
a2 + b2 = (a + b)2 - 2ab
Calculation:
3(a2 + b2)
⇒ 3{(a + b)2 - 2ab}
⇒ 3{52 - 2 × 6}
⇒ 39
∴ The required value is 39.
If x = 4 + √6 and y = 4 - √6 then the value of x2 + y2 is:
Answer (Detailed Solution Below)
Square Identity Question 8 Detailed Solution
Download Solution PDFGiven:
If x = 4 + √6 and y = 4 - √6
Formula used:
x2 + y2 = (x + y)2 - 2xy
Calculation:
x = 4 + √6 and y = 4 - √6
x + y = (4 + √6) + (4 - √6) = 8
x × y = (4 + √6)(4 - √6) = 42 - (√6)2 = 16 - 6 = 10
⇒ x2 + y2 = (8)2 - 2 × 10
⇒ x2 + y2 = 64 - 20
⇒ x2 + y2 = 44
∴ The correct answer is option (3).
Simplify (5z - 7y)2 + (7z + 5y)2 - 49z2
Answer (Detailed Solution Below)
Square Identity Question 9 Detailed Solution
Download Solution PDFGiven:
Simplify (5z - 7y)2 + (7z + 5y)2 - 49z2
Formula used:
(a + b)2 = a2 + 2ab + b2
(a - b)2 = a2 - 2ab + b2
Calculation:
(5z - 7y)2 + (7z + 5y)2 - 49z2
⇒ (25z2 - 2 × 5z × 7y + 49y2) + (49z2 + 2 × 7z × 5y + 25y2) - 49z2
⇒ 25z2 - 70zy + 49y2 + 49z2 + 70zy + 25y2 - 49z2
⇒ 25z2 + 49z2 - 49z2 + 49y2 + 25y2
⇒ 25z2 + 74y2
∴ The correct answer is option (4).
The value of [(.253*.253-.253*.067+.067*.067)/(.253*.253*.253+.067*.067*.067)] is:
Answer (Detailed Solution Below)
Square Identity Question 10 Detailed Solution
Download Solution PDFGiven:
\(\dfrac{(.253 \times .253 - .253 \times .067 + .067 \times .067)}{(.253 \times .253 \times .253 + .067 \times .067 \times .067)}\)
Formula used:
\(\dfrac{a^2 - ab + b^2}{a^3 + b^3}\) = \(\dfrac{{a^2 - ab + b^2}}{(a + b)(a^2 - ab + b^2)}\) = \(\dfrac{1}{a + b}\)
Calculation:
Let a = 0.253 and b = 0.067
⇒ \(\dfrac{{(0.253^2 - 0.253 \times 0.067 + 0.067^2)}}{(0.253 + 0.067)(0.253^2 - 0.253 \times 0.067 + 0.067^2)}\)
⇒ \(\dfrac{1}{0.253 + 0.067}\) = (1 / 0.32)
⇒ \(\)3.125
∴ The value of the given expression is 3.125.
If a + b = 12 and 4ab = 140, then what is the value of a2 + b2?
Answer (Detailed Solution Below)
Square Identity Question 11 Detailed Solution
Download Solution PDFGiven:
If a + b = 12 and 4ab = 140
Formula used:
(a + b)2 = a2 + b2 + 2ab
Calculation:
(a + b)2 = 122
⇒ 144 = a2 + b2 + 2ab
Since, 4ab = 140
⇒ ab = 35
⇒ 144 = a2 + b2 + 2 × 35
⇒ 144 = a2 + b2 + 70
⇒ a2 + b2 = 74
∴ The correct answer is option 2.
Simplify \(\frac{2.46\times 2.46-1.46\times 1.46}{2.46-1.46}\) and select the most appropriate fraction.
Answer (Detailed Solution Below)
Square Identity Question 12 Detailed Solution
Download Solution PDFGiven:
\(\dfrac{(2.46 \times 2.46-1.46 \times 1.46)}{(2.46-1.46)}\)
Formula used:
\((a^2 - b^2) = (a + b)(a - b)\)
Calculation:
⇒ \(\dfrac{(2.46 + 1.46)(2.46 - 1.46)}{(2.46-1.46)}\)
⇒ \(\dfrac{(2.46^2 - 1.46^2)}{(2.46-1.46)}\)
⇒ \((2.46 + 1.46)\)
⇒ 3.92
⇒ \(\dfrac{392}{100}\)
∴ The correct answer is option (2).
Simplify : \(\rm \frac{0.728 \times 0.728-0.272 \times 0.272}{0.456}\)
Answer (Detailed Solution Below)
Square Identity Question 13 Detailed Solution
Download Solution PDFGiven:
Simplify: (0.728 × 0.728 - 0.272 × 0.272) / 0.456
Formula used:
(a2 - b2) = (a + b)(a - b)
Calculation:
(0.728 × 0.728 - 0.272 × 0.272) / 0.456
⇒ (0.7282 - 0.2722) / 0.456
⇒ ((0.728 + 0.272) × (0.728 - 0.272)) / 0.456
⇒ (1.0 × 0.456) / 0.456
⇒ 0.456 / 0.456
⇒ 1
∴ The correct answer is option (2).
Square Identity Question 14:
Which of the following can be the value of k, if \(\frac{(88 \div 8 \times k - 3 \times 3)}{(6^2 - 7 \times 5 + k^2)} = 1\)
Answer (Detailed Solution Below)
Square Identity Question 14 Detailed Solution
Given:
(88 ÷ 8 × k - 3 × 3) / (62 - 7 × 5 + k2) = 1
Formula used:
Equation: Numerator = Denominator
Calculations:
Numerator: 88 ÷ 8 × k - 3 × 3
⇒ 11k - 9
Denominator: 62 - 7 × 5 + k2
⇒ 36 - 35 + k2
⇒ 1 + k2
Setting the equation:
11k - 9 = 1 + k2
⇒ k2 - 11k + 10 = 0
Using the quadratic formula:
k = (-b ± √(b2 - 4ac)) / (2a)
Where a = 1, b = -11, c = 10
⇒ k = (11 ± √((-11)2 - 4 × 1 × 10)) / (2 × 1)
⇒ k = (11 ± √(121 - 40)) / 2
⇒ k = (11 ± √81) / 2
⇒ k = (11 ± 9) / 2
Values of k:
⇒ k = (20 / 2) = 10
⇒ k = (2 / 2) = 1
∴ The possible values of k are 10 and 1.
Square Identity Question 15:
Simplify: \(\sqrt {36{x^2} - 108x + 81} \).
Answer (Detailed Solution Below)
Square Identity Question 15 Detailed Solution
Calculations:
√(36x² - 108x + 81)
=√[(6x)² - 2 × 6 × 9x + (9)²]
= √[6x - 9]²
= 6x - 9
Hence, The Required value is 6x - 9.