Quantitative Aptitude

Simplification and Approximation

647 Questions
All Approximate with option-sensitive rounding 386 Percentage calculation 112 Calculate squares and identify square roots 38 Simplify surds and indices 29 VBODMAS 27 Recognize algebraic identity patterns 23 Use cube patterns and perfect cube roots 15 Fraction and mixed number reduction 13 Mixed recurring decimals 3 Integer division and remainders 1

Simplification and Approximation Questions

Multiple choice

The approximate value of $\sqrt [ 5 ]{ 33 } $ is
  1. $2.0125$
  2. $2.1$
  3. $2.01$
  4. $3.258$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We want the 5th root of 33. Since 2^5 = 32, the 5th root of 33 is slightly larger than 2. Using the binomial approximation (32+1)^(1/5) = 32^(1/5) * (1 + 1/32)^(1/5) = 2 * (1 + 1/160) = 2 + 2/160 = 2 + 0.0125 = 2.0125.

Multiple choice

The approximate value of $(1.0002)^{3000}$ is

  1. 1.2

  2. 1.4

  3. 1.6

  4. 1.8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using the binomial approximation (1 + x)^n is approximately 1 + nx for small x. Here, (1 + 0.0002)^3000 is approximately 1 + (3000 * 0.0002) = 1 + 0.6 = 1.6.

Multiple choice

If the value of the expression $\displaystyle \frac { x-12 }{ \sqrt { 8 } } $ can be approximated to be equal to $\displaystyle \frac { x\sqrt { 2 } }{ 4 } -C$, then determine the value of $C$ in the equation.
  1. $-3$
  2. $\displaystyle -\sqrt { 3 } $
  3. $2$
  4. $\displaystyle 3\sqrt { 2 } $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

(x-12)/sqrt(8) = (x-12)/(2*sqrt(2)) = x/(2*sqrt(2)) - 12/(2*sqrt(2)) = x*sqrt(2)/4 - 6/sqrt(2) = x*sqrt(2)/4 - 3*sqrt(2). Comparing with x*sqrt(2)/4 - C, we get C = 3*sqrt(2).

Multiple choice

Triangle $ABC$ is a right triangle with sides of length $4, 6$ and $x$. If $4 < x < 6$, what is the approximate value of $x$?
  1. $4$
  2. $4.47$
  3. $5.21$
  4. $5.63$
  5. $7.21$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a right triangle with sides 4, 6, and x, x is either a leg or the hypotenuse. If x is a leg, x^2 + 4^2 = 6^2 => x^2 = 36-16=20 => x = sqrt(20) approx 4.47. If x is the hypotenuse, 4^2 + 6^2 = x^2 => 16+36=52 => x = sqrt(52) approx 7.21. Given 4 < x < 6, 4.47 is the correct value.

Multiple choice

Find the square root of $0.007225$
  1. $0.085$
  2. $0.088$
  3. $0.087$
  4. $0.082$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The square root of 7225 is 85. Since there are 6 decimal places in 0.007225, the square root must have 3 decimal places, resulting in 0.085.

Multiple choice

Find the square root of $4.2025$
  1. $2.05$
  2. $2.08$
  3. $3.01$
  4. $2.09$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To find the square root of 4.2025, note that 2.0^2 = 4 and 2.1^2 = 4.41. Since the last digit is 5, the root must end in 5, making 2.05 the correct value.