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Sq Root (Math) Solved Questions & Notes (2026) - Apex Rankers

General Competitive Exams > Math > Sq Root

15 Total Solved Questions
~23 mins Estimated Reading Time
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Sq Root

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Q. 1 Quantitative Aptitude Test
Difficulty: Medium (1 Mark)
Solve:
\(\frac{\sqrt{24}+\sqrt{216}}{\sqrt{96}}=?\)
A
\(2/\sqrt{6}\)
B
2
✓ Correct
C
\(2\sqrt{6}\)
D
\(6\sqrt{2}\)
💡 Step-by-Step Explanation & Concept Rationale
Simplify each radical by pulling out perfect square factors:
\(\sqrt{24} = \sqrt{4 \times 6} = 2\sqrt{6}\)
\(\sqrt{216} = \sqrt{36 \times 6} = 6\sqrt{6}\)
\(\sqrt{96} = \sqrt{16 \times 6} = 4\sqrt{6}\)

Substitute these simplified forms back into the expression:
\(\frac{2\sqrt{6}+6\sqrt{6}}{4\sqrt{6}}=\frac{8\sqrt{6}}{4\sqrt{6}}=2\)
Q. 2 Quantitative Aptitude Test
Difficulty: Medium (1 Mark)
Solve:
\(\sqrt{\frac{0.289}{0.00121}}=?\)
A
\(\frac{170}{11}\)
✓ Correct
B
\(\frac{0.17}{11}\)
C
\(\frac{17}{110}\)
D
\(\frac{17}{11}\)
💡 Step-by-Step Explanation & Concept Rationale
Multiply the top and bottom values inside the radical by 100,000 to eliminate the decimal points:
\(\sqrt{\frac{28900}{121}}\)
Separate the square root for the numerator and the denominator:
\(\frac{\sqrt{28900}}{\sqrt{121}}=\frac{170}{11}\)
Q. 3 Quantitative Aptitude Test
Difficulty: Medium (1 Mark)
Solve:
\(\sqrt{\frac{?}{169}}=\frac{54}{39}\)
A
2916
B
324
✓ Correct
C
108
D
4800
💡 Step-by-Step Explanation & Concept Rationale
Let the unknown variable be \(x\). Split the square root between the numerator and denominator:
\(\frac{\sqrt{x}}{\sqrt{169}}=\frac{54}{39}\)
Since \(\sqrt{169} = 13\), substitute it into the equation:
\(\frac{\sqrt{x}}{13}=\frac{54}{39}\)
Isolate \(\sqrt{x}\) by multiplying both sides by 13:
\(\sqrt{x}=\frac{54\times 13}{39}\)
Simplify the fraction (since \(39 \div 13 = 3\)):
\(\sqrt{x}=\frac{54}{3}=18\)
Square both sides to find \(x\):
\(x=18^{2}=324\)
Q. 4 Quantitative Aptitude Test
Difficulty: Medium (1 Mark)
Solve:
\(\sqrt{\frac{1}{9}}=?\)
A
\(\frac{1}{\sqrt{3}}\)
B
\(\frac{3}{1}\)
C
\(\sqrt{\frac{1}{18}}\)
D
\(\frac{1}{3}\)
✓ Correct
💡 Step-by-Step Explanation & Concept Rationale
Take the square root of the numerator and the denominator separately:
\(\sqrt{\frac{1}{9}}=\frac{\sqrt{1}}{\sqrt{9}}=\frac{1}{3}\)
Q. 5 Quantitative Aptitude Test
Difficulty: Medium (1 Mark)
Solve:
\(\sqrt{3721}=?\)
A
186.5
B
7442
C
1860.5
D
61
✓ Correct
💡 Step-by-Step Explanation & Concept Rationale
$\sqrt{3721​}=61$.
Verified by 61×61=3721.
📜 Instructions / Reading Passage
10 Questions in this set
SQUARE ROOTS & SIMPLIFICATION: Solve the following multiple-choice questions by calculating the exact square roots or simplifying the provided arithmetic expressions.
Q. 6 Quantitative Aptitude Test
Difficulty: Medium (1 Mark)
Find the square root of 213444
A
362
B
482
C
462
✓ Correct
D
442
💡 Step-by-Step Explanation & Concept Rationale
213444​=462. Verified by 462×462=213444.
Q. 7 Quantitative Aptitude Test
Difficulty: Medium (1 Mark)
Find the square root of 5625/5929
A
75/77
✓ Correct
B
72/77
C
65/72
D
75/65
💡 Step-by-Step Explanation & Concept Rationale
5625​=75 and 5929​=77. Thus, result is 75/77.
Q. 8 Quantitative Aptitude Test
Difficulty: Medium (1 Mark)
Find the square root of 543169
A
737.5
✓ Correct
B
737
C
727
D
627
💡 Step-by-Step Explanation & Concept Rationale
543169​=737. Verified by 737×737=543169.
Q. 9 Quantitative Aptitude Test
Difficulty: Medium (1 Mark)
Find the square root of 1227.8016
A
35.04
✓ Correct
B
32.65
C
35.06
D
32.04
💡 Step-by-Step Explanation & Concept Rationale
1227.8016​=35.04.
Q. 10 Quantitative Aptitude Test
Difficulty: Medium (1 Mark)
Find the square root of 1809025
A
1255
B
1355
C
1245
D
1345
✓ Correct
💡 Step-by-Step Explanation & Concept Rationale
1809025​=1345.
Q. 11 Quantitative Aptitude Test
Difficulty: Medium (1 Mark)
Find the square root of .00002601
A
0.0051
✓ Correct
B
0.0053
C
0.0059
D
0.0062
💡 Step-by-Step Explanation & Concept Rationale
.00002601​=0.0051. Move decimal 4 places for root of 8 places.
Q. 12 Quantitative Aptitude Test
Difficulty: Medium (1 Mark)
Find the square root of $3\frac{3}{7}$
A
1.9
B
1.85
✓ Correct
C
1.68
D
1.28
💡 Step-by-Step Explanation & Concept Rationale
$3\frac{3}{7}$​=24/7≈3.428.
3.428​≈1.85.
Q. 13 Quantitative Aptitude Test
Difficulty: Medium (1 Mark)
What must be subtracted from 8934 to make it a perfect square?
A
98
✓ Correct
B
100
C
97
D
88
💡 Step-by-Step Explanation & Concept Rationale
Nearest square is 942=8836. 8934−8836=98.
Q. 14 Quantitative Aptitude Test
Difficulty: Medium (1 Mark)
What must be added to 5678 to make it a perfect square?
A
100
B
98
✓ Correct
C
88
D
78
💡 Step-by-Step Explanation & Concept Rationale
Next square is 762=5776. 5776−5678=98.
Q. 15 Quantitative Aptitude Test
Difficulty: Medium (1 Mark)
Find the square root of 18671041
A
4321
✓ Correct
B
4222
C
4223
D
4121
💡 Step-by-Step Explanation & Concept Rationale
18671041​=4321.
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