Square Identity MCQ Quiz - Objective Question with Answer for Square Identity - Download Free PDF

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).

Given:

Formula used:

= =

Calculation:

Let a = 0.253 and b = 0.067

⇒

⇒  = (1 / 0.32)

⇒ 3.125

∴ The value of the given expression is 3.125.

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.

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).

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).

Calculations:

√(36x² - 108x + 81)

=√[(6x)² - 2 × 6 × 9x + (9)²]

= √[6x - 9]²

= 6x - 9

Hence, The Required value is 6x - 9.

Given:

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.

Given:

Formula used:

= =

Calculation:

Let a = 0.253 and b = 0.067

⇒

⇒  = (1 / 0.32)

⇒ 3.125

∴ The value of the given expression is 3.125.

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.

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).

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.

Calculations:

√(36x² - 108x + 81)

=√[(6x)² - 2 × 6 × 9x + (9)²]

= √[6x - 9]²

= 6x - 9

Hence, The Required value is 6x - 9.

Given:

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.

Given:

Expression =

Formula used:

The given expression can be simplified by using the identity for the sum of squares and products:

Here, a = 1.5, b = 2.5, and c = 3.5.

Calculations:

⇒ 

⇒ 

Using formula, 

⇒ 

⇒ 

(a + b + c) = 1.5 + 2.5 + 3.5 = 7.5

The value of the given expression is 7.5.

Given:

a² + b² = 148

ab = 54

Formula used:

(a + b)² = a² + b² + 2ab

(a - b)² = a² + b² - 2ab

Calculations:

(a + b)² = 148 + 2 × 54

⇒ (a + b)² = 148 + 108 = 256

(a - b)² = 148 - 2 × 54

⇒ (a - b)² = 148 - 108 = 40

⇒

⇒

Verification of options:

Option 1: (Correct)

Option 2: (Incorrect)

Option 3: (Incorrect)

Option 4: (Incorrect)

∴ The correct answer is option (1).