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

Last updated on May 28, 2025

The square of a number is obtained by multiplying the number by itself. When natural numbers are taken then it is called the perfect square of that number. Eg. Square of 2 is 4, Square of 4 is 16 etc.The Square root of a number y is that number which when multiplied by itself gives y as the product. Eg. 3 is the square root of 9. We must follow important points to solve these problems i. e. A number having 2, 3, 7, 8 at unit place is never a perfect square. The squares of odd numbers are odd and the squares of even numbers are even. A number ending with an odd number of zeroes is never a perfect square. For solving the square root of any number, we can use two methods i

Latest Square and Square Root MCQ Objective Questions

Square and Square Root Question 1:

Square root of \(\frac{0.081}{0.0064}\times \frac{0.484}{6.25}\times \frac{2.5}{12.1}\ \) is:

  1. 0.45
  2. 0.34
  3. 0.75
  4. 0.55
  5. None of the above

Answer (Detailed Solution Below)

Option 1 : 0.45

Square and Square Root Question 1 Detailed Solution

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

Square and Square Root Question 2:

\(\sqrt{\sqrt{156.25}\times 1.2^2\times 2.5+\sqrt{361}}\) Solve the question.

  1. 7
  2. 9
  3. 8
  4. 64
  5. None of the above

Answer (Detailed Solution Below)

Option 3 : 8

Square and Square Root Question 2 Detailed Solution

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).

Square and Square Root Question 3:

If a = \(\frac{\sqrt{5}+1}{\sqrt{5}−1}\) and b = \(\frac{\sqrt{5}−1}{\sqrt{5}+1}\), then \(\frac{1+\frac{b}{a}+\frac{b^{2}}{a^{2}}}{1−\frac{b}{a}+\frac{b^{2}}{a^{2}}}\) equals :

  1. \(\frac{5}{4}\)
  2. \(​\frac{7}{3}\)
  3. \(\frac{4}{3}\)
  4. 1
  5. None of the above

Answer (Detailed Solution Below)

Option 3 : \(\frac{4}{3}\)

Square and Square Root Question 3 Detailed Solution

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

Square and Square Root Question 4:

If \(\sqrt{2916} \) = 54 then what is the value of the following?

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

  1. 5.999
  2. 6.00
  3. 5.9994
  4. 5.90
  5. None of the above

Answer (Detailed Solution Below)

Option 3 : 5.9994

Square and Square Root Question 4 Detailed Solution

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.

Square and Square Root Question 5:

If \(\frac{{32\,\, \times \,\,4\,\, + \,\,\sqrt x }}{{38}}\)= 4, then the value of x is

  1. 576
  2. 196
  3. 256
  4. 296
  5. None of the above

Answer (Detailed Solution Below)

Option 1 : 576

Square and Square Root Question 5 Detailed Solution

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.

Top Square and Square Root MCQ Objective Questions

 If \(\sqrt{14.44}\) + \(\sqrt{(9 + x^2)}\) = 8.8, then find the value of x.

  1. 5
  2. 4
  3. 7
  4. 2

Answer (Detailed Solution Below)

Option 2 : 4

Square and Square Root Question 6 Detailed Solution

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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.

What is the least number to be added to 4523 to make it a perfect square?

  1. 101
  2. 105
  3. 110
  4. 238

Answer (Detailed Solution Below)

Option 1 : 101

Square and Square Root Question 7 Detailed Solution

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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".

What is the square root of 9 + \(2\sqrt{14}\) ?

  1. 1 + \(2\sqrt 2\)
  2. \(\sqrt 3\)\(\sqrt 6\)
  3. \(\sqrt 2\)\(\sqrt 7\)
  4. \(\sqrt 2\)\(\sqrt 5\)

Answer (Detailed Solution Below)

Option 3 : \(\sqrt 2\)\(\sqrt 7\)

Square and Square Root Question 8 Detailed Solution

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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.

\(\sqrt[3]{{5\frac{{23}}{{64}}}} \) is equal to:

  1. 1.57
  2. 1.75
  3. 2.75
  4. 1.25

Answer (Detailed Solution Below)

Option 2 : 1.75

Square and Square Root Question 9 Detailed Solution

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

Simplify: \(\frac{(76+84)^2-(76-84)^2}{76 \times 84}\) = ?

  1. 4
  2. 9
  3. 8
  4. 6

Answer (Detailed Solution Below)

Option 1 : 4

Square and Square Root Question 10 Detailed Solution

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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

If \( x=\sqrt{3018+\sqrt{36+\sqrt{169}}}\), then what is the value of x?

  1. 42
  2. 44
  3. 55
  4. 45

Answer (Detailed Solution Below)

Option 3 : 55

Square and Square Root Question 11 Detailed Solution

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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

The correct option is 3 i.e. 55

The square root of 27225 is:

  1. 165
  2. 175
  3. 155
  4. 145

Answer (Detailed Solution Below)

Option 1 : 165

Square and Square Root Question 12 Detailed Solution

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Square root of 27225

Using factorization:

27225 = 3 × 3 × 5 × 5 × 11 × 11

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

∴ √27225 = 165  

Square root of 0.9 is equal to

  1. 0.9487
  2. 0.3
  3. 0.9463
  4. 0.03

Answer (Detailed Solution Below)

Option 1 : 0.9487

Square and Square Root Question 13 Detailed Solution

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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.

The value of \(\sqrt{400}+\sqrt{0.0400}+\sqrt{0.0004}\) is -

  1. 20.202
  2. 20.022
  3. 0.22
  4. 20.22

Answer (Detailed Solution Below)

Option 4 : 20.22

Square and Square Root Question 14 Detailed Solution

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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

If the positive square root of (5 + 3√2) (5 - 3√2) is α, then what is the positive square root of 8 + 2α ?  

  1. 2 + √3
  2. 3 - √2
  3. √7 - 1
  4. √7 + 1

Answer (Detailed Solution Below)

Option 4 : √7 + 1

Square and Square Root Question 15 Detailed Solution

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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

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