Mathematics/General Ability MCQs
Topic Notes: Mathematics/General Ability
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
51
Simplify completely: sqrt(16x^4)
Answer:
4x^2
Evaluate the numerical and variable parts separately. The square root of 16 is 4, and the square root of x^4 is x^2. This gives the exact simplified form 4x^2.
52
Simplify: sqrt(y^5)
Answer:
y^2*sqrt(y)
Rewrite y^5 as the product of the largest perfect square (y^4) and y. The square root of y^4 is y^2, bringing it outside the radical to get y^2*sqrt(y).
53
Simplify the expression containing a variable: sqrt(x^3)
Answer:
x*sqrt(x)
Separate x^3 into x^2 * x. Since x^2 is a perfect square, taking its square root gives x on the outside, leaving one x inside the radical: x*sqrt(x).
54
Simplify: cbrt(54)
Answer:
3*cbrt(2)
The number 54 can be divided by the perfect cube 27 (27 * 2 = 54). Evaluating the cube root of 27 gives 3, so the expression simplifies to 3*cbrt(2).
55
Simplify the cube root: cbrt(16)
Answer:
2*cbrt(2)
Look for a perfect cube factor of 16, which is 8. Writing cbrt(16) as cbrt(8 * 2) allows us to bring out the cube root of 8 (which is 2), yielding 2*cbrt(2).
56
Simplify the radical: sqrt(20)
Answer:
2*sqrt(5)
Factor 20 into a perfect square and another number, which is 4 * 5. Taking the square root of 4 gives 2, which leaves us with the simplified form 2*sqrt(5).
57
Simplify: sqrt(48)
Answer:
4*sqrt(3)
The number 48 can be factored into 16 * 3. Because 16 is a perfect square, its square root (4) can be brought outside the radical, resulting in 4*sqrt(3).
58
Simplify the expression: sqrt(72)
Answer:
6*sqrt(2)
Find the highest perfect square factor of 72, which is 36. Since 72 = 36 * 2, we take the square root of 36 to get 6 outside, leaving 6*sqrt(2).
59
Simplify: sqrt(27)
Answer:
3*sqrt(3)
The largest perfect square that divides 27 is 9. We can write sqrt(27) as sqrt(9 * 3). The square root of 9 is 3, making the simplified form 3*sqrt(3).
60
Simplify the radical expression: sqrt(50)
Answer:
5*sqrt(2)
To simplify sqrt(50), find the largest perfect square factor of 50, which is 25. Rewrite sqrt(50) as sqrt(25 * 2), which simplifies to 5*sqrt(2).