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

Given:

Square root of \(\frac{0.081}{0.0064}× \frac{0.484}{6.25}× \frac{2.5}{12.1}\ \)

Calculation:

⇒ \(\sqrt{\frac{0.081}{0.0064}× \frac{0.484}{6.25}× \frac{2.5}{12.1}}\ \) 

⇒ \(\sqrt{\frac{81}{64}× \frac{484}{625}× \frac{25}{121}}\ \)

⇒ 9/8 × 22/25 × 5/11

⇒ 9/20

⇒ 0.45

∴ \(\sqrt{\frac{0.081}{0.0064}× \frac{0.484}{6.25}× \frac{2.5}{12.1}}\ \) = 0.45

Given:

\(\sqrt{\sqrt{156.25}\times 1.2^2\times 2.5+\sqrt{361}}\)

Formula used:

Order of operations (BODMAS): Evaluate powers, roots, multiplication, and addition step-by-step.

Calculation:

\(\sqrt{\sqrt{156.25}\times 1.2^2\times 2.5+\sqrt{361}}\)

⇒ √(√156.25 × 1.44 × 2.5 + √361)

⇒ √(12.5 × 1.44 × 2.5 + 19)

⇒ √(12.5 × 3.6 + 19)

⇒ √(45 + 19)

⇒ √64

⇒ 8

∴ The correct answer is option (3).

Given:

If a = \(\frac{√{5}+1}{√{5}−1}\) and b = \(\frac{√{5}−1}{√{5}+1}\), 

Calculation:

If a = \(\frac{√{5}+1}{√{5}−1}\) and b = \(\frac{√{5}−1}{√{5}+1}\), 

Here, ab = 1 and

a + b = [(√5 + 1)² + (√5 -1)²]/4 = (5 + 1 + 2√5 + 5 + 1 - 2√5)/4 = 3

(a² + b²) = (a + b)² - 2ab = 9 - 2 = 7

∴ \(\frac{1+\frac{b}{a}+\frac{b^{2}}{a^{2}}}{1−\frac{b}{a}+\frac{b^{2}}{a^{2}}}\)= (7 + 1)/(7 - 1) = 8/6 = 4/3

Given:

 \(\sqrt{2916} \) = 54 

Calculations:

 \(\sqrt{29.16}+\sqrt{0.2916}+ \sqrt{0.002916} +\sqrt{0.00002916}\)

= 5.4  + 0.54 + 0.054 + 0.0054

= 5.4 + 0.54 + 0.0594

= 5.4 + 0.5994

= 5.9994

Hence, The simplified value is 5.9994.

Calculation:       

\(\frac{{32\,\, × \,\,4\,\, + \,\,\sqrt x }}{{38}}\) = 4

By cross multiplication:

⇒ 32 × 4 + \(\sqrt{x}\) = 38 × 4

\(⇒ \sqrt{x}\) = 38 × 4 - 32 × 4

\(⇒ \sqrt{x}\) = 4 × (38 - 32)

\(⇒ \sqrt{x}\) = 4 × 6

Squaring both the sides

\(⇒ (\sqrt{x}\))² = (4 × 6)²

⇒ x = 576

∴The value of x is 576.

Calculation:

⇒ √14.44 + √(9 + x²) = 8.8

⇒ 3.8 + √(9 + x2) = 8.8

⇒ √(9 + x2) = 8.8 - 3.8

⇒ √(9 + x2) = 5

⇒ 9 + x² = 25 

⇒ x2 = 25 - 9

⇒ x2 = 16

⇒ x = 4

∴ The value of x is 4.

The square of the numbers are

(66)² = 4356

(67)² = 4489

(68)² = 4624

So, the least number to be added = 4624 - 4523 = 101

Hence, the correct answer is "101".

Given:

The square root of 9 + \(2√{14}\)

Concept used:

(a + b)² = a² + b² + 2ab

Calculation:

We have,

⇒ 9 + \(2√{14}\) 

⇒ 2 + 7 + 2√(2 × 7)

⇒ (√2)² + (√7)² + 2 × √2 × √7

Now, according to the above concept,

⇒ (√2 + √7)²

∴ The required square root is √2 + √7.

 \(\sqrt[3]{{5+\frac{{23}}{{64}}}} \) = \(\sqrt[3]{{\frac{320}{64}+\frac{{23}}{{64}}}} \) = \(\sqrt[3]{{\frac{343}{64}}} \) = 7/4 = 1.75

Given:

\(\dfrac{(76+84)^2-(76-84)^2}{76 \times 84}\)

Formula used:

(a + b)² - (a - b)² = 4ab

Calculations:

(a + b)2 - (a - b)2 

⇒ a² + b² + 2ab - {a² + b² - 2ab}

⇒ 2ab + 2ab = 4ab

Now, \(\dfrac{(76+84)^2-(76-84)^2}{76 \times 84}\)

⇒ \(\dfrac{4 × 76 × 84}{76 × 84}\) = 4

∴ The answer is 4

Calculation:  

 \(\sqrt{}169 = 13\)  

\(\sqrt{}36 = 6\)

According to the question: 

\(x=\sqrt{3018+\sqrt{36+\sqrt{169}}}\)

\(x=\sqrt{3018+\sqrt{36+13}}\)

\(x=\sqrt{3018+7}\)

\(⇒ x=\sqrt{3025}\)

⇒ x  = 55

Square root of 27225

Using factorization:

27225 = 3 × 3 × 5 × 5 × 11 × 11

∴ Square root will be = 3 × 5 × 11 = 165

∴ √27225 = 165  

Concept used:

\(\sqrt {10} \approx 3.1622\)

Calculation:

\(\sqrt {0.9}\)

⇒ \(\sqrt {\frac {9}{10}}\)

⇒ \({\frac {3}{3.1622}}\) ≈ 0.9487

∴ The square root of 0.9 is equal to 0.9487.

Given:

\(\sqrt{400}+\sqrt{0.0400}+\sqrt{0.0004}\)

Calculations:

\(\sqrt{400}+\sqrt{0.0400}+\sqrt{0.0004}\)

⇒ 20 + 0.2 + 0.02

⇒ 20.22

∴ The answer is 20.22

Formula used:

(a - b) (a + b) = a² - b²

(a² + 2ab + b²) = (a + b)²

Calculation:

 Given that,

α  = √[(5 + 3√2) (5 - 3√2)]

Since, (a - b) (a + b) = a2 - b2

α = √[(5² - (3√2)²]

α = √(25 - 18) = √7

Let the required square root is β 

β = √(8 + 2√7) = √(7 + 1 + 2√7)

β = √[(√7)² + 2.1.√7 +  (1)²]

β = √(√7 + 1)² 

Since, (a2 + 2ab + b2) = (a + b)2

β = √7 + 1