Square and Square Root MCQ Quiz - Objective Question with Answer for Square and Square Root - Download Free PDF
Last updated on May 28, 2025
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:
Answer (Detailed Solution Below)
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.
Answer (Detailed Solution Below)
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 :
Answer (Detailed Solution Below)
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?
\(\sqrt{29.16} \) + \(\sqrt{0.2916}\) + \(\sqrt{0.002916}\) + \(\sqrt{0.00002916}\)
Answer (Detailed Solution Below)
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
Answer (Detailed Solution Below)
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.
Answer (Detailed Solution Below)
Square and Square Root Question 6 Detailed Solution
Download Solution PDFCalculation:
⇒ √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?
Answer (Detailed Solution Below)
Square and Square Root Question 7 Detailed Solution
Download Solution PDFThe 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 + \(2\sqrt{14}\) ?
Answer (Detailed Solution Below)
Square and Square Root Question 8 Detailed Solution
Download Solution PDFGiven:
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:
Answer (Detailed Solution Below)
Square and Square Root Question 9 Detailed Solution
Download Solution PDF\(\sqrt[3]{{5+\frac{{23}}{{64}}}} \) = \(\sqrt[3]{{\frac{320}{64}+\frac{{23}}{{64}}}} \) = \(\sqrt[3]{{\frac{343}{64}}} \) = 7/4 = 1.75
Simplify: \(\frac{(76+84)^2-(76-84)^2}{76 \times 84}\) = ?
Answer (Detailed Solution Below)
Square and Square Root Question 10 Detailed Solution
Download Solution PDFGiven:
\(\dfrac{(76+84)^2-(76-84)^2}{76 \times 84}\)
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?
Answer (Detailed Solution Below)
Square and Square Root Question 11 Detailed Solution
Download Solution PDFCalculation:
\(\sqrt{}169 = 13\)
\(\sqrt{}36 = 6\)
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. 55The square root of 27225 is:
Answer (Detailed Solution Below)
Square and Square Root Question 12 Detailed Solution
Download Solution PDFSquare 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
Answer (Detailed Solution Below)
Square and Square Root Question 13 Detailed Solution
Download Solution PDFConcept 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 -
Answer (Detailed Solution Below)
Square and Square Root Question 14 Detailed Solution
Download Solution PDFGiven:
\(\sqrt{400}+\sqrt{0.0400}+\sqrt{0.0004}\)
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 ?
Answer (Detailed Solution Below)
Square and Square Root Question 15 Detailed Solution
Download Solution PDFFormula 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