This set of Aptitude Questions and Answers (MCQs) focuses on “Square Roots and Cube Roots”. These questions are beneficial for various competitive exams, placement interviews, and entrance tests.
1. If x=2+√3 and y=2-√3, then find the value of x2+y2.
a) 14
b) 8
c) 16
d) 12
View Answer
Explanation: x2+y2=(2+√3)2+(2-√3)2=2\(\Big[2^2+(√3)^2\Big]\)=14.
2. Find the value of \(\sqrt{\frac{10.5*1.19*560}{0.21*1.7}}\).
a) 225
b) 140
c) 375
d) 300
View Answer
Explanation: \(\sqrt{\frac{10.5*1.19*560}{0.21*1.7}}=\sqrt{\frac{105*119*560}{21*17}}=\sqrt{5*7*560}\)=140.
3. Find the smallest number that must be added to 1760 to make it a perfect square.
a) 6
b) 8
c) 4
d) 1
View Answer
Explanation: Number to be added = 422 – 1760 = 1764 – 1760 = 4.
4. Find the \(\sqrt{12+\sqrt{12+\sqrt{12+⋯}}}\).
a) 5
b) 4.5
c) 3.9
d) 4
View Answer
Explanation: Let x = \(\sqrt{12+\sqrt{12+\sqrt{12+⋯}}}\)
\(\sqrt{12+x}\)=x 🡪 12+x=x2 🡪 x2-x-12=0 🡪 (x-4)(x+3)=0 🡪 x = 4.
5. Find the value of \(\sqrt{(\sqrt{13456}+\sqrt{11881})}\).
a) 15
b) 17
c) 19
d) 13
View Answer
Explanation: \(\sqrt{(\sqrt{13456}+\sqrt{11881})}=\sqrt{116+109}=\sqrt{225}\)=15.
6. Find the square root of 12345654321.
a) 11111
b) 111111
c) 111111
d) 191919
View Answer
Explanation: Square root of 12345654321 = 111111.
7. Find the number of digits in the square root of 15243606235.
a) 5
b) 7
c) 6
d) 8
View Answer
Explanation: The number of digits in the square root of a perfect square number of n digits is \(\frac{n+1}{2}\), if n is odd.
Therefore, the number of digits in the square root of 15243606235 for n = 11 is \(\frac{11+1}{2}\)=6.
8. Find the number of digits in the square root of 97357689.
a) 6
b) 7
c) 5
d) 4
View Answer
Explanation: The number of digits in the square root of a perfect square number of n digits is \(\frac{n}{2}\), if n is even.
Therefore, the number of digits in the square root of 97357689 for n = 8 is \(\frac{8}{2}\)=4.
9. One-third of the sum of all prime numbers greater than 2 but less than 20, is the square of which number?
a) 5
b) 6
c) 7
d) 9
View Answer
Explanation: The sum of prime numbers greater than 2 but less than 20 = 3+5+7+11+13+17+19 = 75.
One-third of the sum of prime numbers greater than 2 but less than 20 = 75/3 = 25, which is the square of 5.
10. If p*q=p+q+\(\sqrt{2pq}\), then find the value of 3*6.
a) 16
b) 15
c) 12
d) 18
View Answer
Explanation: 3*6=3+6+\(\sqrt{2*3*6}\)=9+√36=9+6=15.
More Aptitude Questions and Answers on Square Roots and Cube Roots:
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