Q. 1
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Solve:
\(\frac{\sqrt{24}+\sqrt{216}}{\sqrt{96}}=?\)
\(\frac{\sqrt{24}+\sqrt{216}}{\sqrt{96}}=?\)
💡
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:
\(\frac{2\sqrt{6}+6\sqrt{6}}{4\sqrt{6}}=\frac{8\sqrt{6}}{4\sqrt{6}}=2\)
\(\sqrt{24} = \sqrt{4 \times 6} = 2\sqrt{6}\)
\(\sqrt{216} = \sqrt{36 \times 6} = 6\sqrt{6}\)
\(\sqrt{96} = \sqrt{16 \times 6} = 4\sqrt{6}\)
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:
\(\sqrt{\frac{0.289}{0.00121}}=?\)
\(\sqrt{\frac{0.289}{0.00121}}=?\)
💡
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:
\(\frac{\sqrt{28900}}{\sqrt{121}}=\frac{170}{11}\)
\(\sqrt{\frac{28900}{121}}\)
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:
\(\sqrt{\frac{?}{169}}=\frac{54}{39}\)
\(\sqrt{\frac{?}{169}}=\frac{54}{39}\)
💡
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 \(x\):
\(x=18^{2}=324\)
\(\frac{\sqrt{x}}{\sqrt{169}}=\frac{54}{39}\)
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:
\(\sqrt{\frac{1}{9}}=?\)
\(\sqrt{\frac{1}{9}}=?\)
💡
Step-by-Step Explanation & Concept Rationale
Take the square root of the numerator and the denominator separately:
\(\sqrt{\frac{1}{9}}=\frac{\sqrt{1}}{\sqrt{9}}=\frac{1}{3}\)
\(\sqrt{\frac{1}{9}}=\frac{\sqrt{1}}{\sqrt{9}}=\frac{1}{3}\)
Q. 5
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Solve:
\(\sqrt{3721}=?\)
\(\sqrt{3721}=?\)
💡
Step-by-Step Explanation & Concept Rationale
$\sqrt{3721}=61$.
Verified by 61×61=3721.
Verified by 61×61=3721.
Q. 6
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Find the square root of 213444
💡
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
💡
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
💡
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
💡
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
💡
Step-by-Step Explanation & Concept Rationale
1809025=1345.
Q. 11
Quantitative Aptitude Test
Difficulty: Medium
(1 Mark)
Find the square root of .00002601
💡
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 $3\frac{3}{7}$
💡
Step-by-Step Explanation & Concept Rationale
$3\frac{3}{7}$=24/7≈3.428.
3.428≈1.85.
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?
💡
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?
💡
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
💡
Step-by-Step Explanation & Concept Rationale
18671041=4321.
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