Square Roots & Cube Roots · Exercise 4 of 6
65 mixed-level square root and cube root questions in the style of IBPS/SBI ("√? = …"), SSC CGL/CHSL, RRB NTPC and Group D, UPSC CSAT, state exams and campus placements. Use them as a timed speed drill.
Find √(25/36) + ∛(8/27).
√(25/36) = 5/6
∛(8/27) = 2/3 = 4/6
5/6 + 4/6 = 9/6 = 3/2
Answer: 3/2
Find √1296 ÷ √36 × √9.
√1296 = 36, √36 = 6, √9 = 3
Left to right: 36 ÷ 6 = 6
6 × 3 = 18
Answer: 18
How many four-digit perfect squares end in 25?
A square ends in 25 only if its root ends in 5.
Four-digit squares have roots 32 – 99
Roots ending in 5: 35, 45, 55, 65, 75, 85, 95 → 7
Answer: 7
√500 lies between which two consecutive integers?
22² = 484 and 23² = 529
484 < 500 < 529
So 22 < √500 < 23
Answer: 22 and 23
What is the total surface area of a cube whose volume is 1,331 cm³?
Edge = ∛1,331 = 11 cm
Surface area = 6 × edge²
= 6 × 121 = 726 cm²
Answer: 726 cm²
Find √64 − ∛64.
√64 = 8
∛64 = 4
8 − 4 = 4
Answer: 4
If 125² = 15625, find √1.5625 × √0.015625.
√1.5625 = 1.25
√0.015625 = 0.125
1.25 × 0.125 = 0.15625
Answer: 0.15625
What is the least natural number x for which √(18 × 14 × x) is an integer?
18 × 14 = 252 = 2² × 3² × 7
Only 7 is unpaired
x = 7 → 252 × 7 = 1,764 = 42²
Answer: 7
Find (√64 + ∛125)².
√64 = 8
∛125 = 5
8 + 5 = 13
13² = 169
Answer: 169
Find the square root of 2,304 by prime factorisation.
2,304 = 2⁸ × 3²
Halve each power: 2⁴ × 3
= 16 × 3 = 48
Answer: 48
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