20 Minutes Test: Square and Cube Root 2 - GMAT MCQ

We need to find the cube root of 0.000216.

Step 1: Convert the decimal to a fraction:
0.000216 = 216 / 1000000

Step 2: Take the cube root of both numerator and denominator:
∛(216 / 1000000) = ∛216 / ∛1000000

• Cube root of 216 = 6 (since 6 × 6 × 6 = 216)

• Cube root of 1000000 = 100 (since 100 × 100 × 100 = 1000000)

So,
∛0.000216 = 6 / 100 = 0.06

so x²=8x6x3
x²=144
x=12

L.C.M. of 21, 36, 66 = 2772.

Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11

To make it a perfect square, it must be multiplied by 7 x 11.

So, required number = 2² x 3² x 7² x 11² = 213444

We are given the value of a = 0.1039, and we need to evaluate the expression:

√( 4a² - 4a + 1 ) + 3a

First, calculate 4a² - 4a + 1:

4a² = 4 × (0.1039)² = 4 × 0.01079681 = 0.04318724
-4a = -4 × 0.1039 = -0.4156
4a² - 4a + 1 = 0.04318724 - 0.4156 + 1 = 0.62758724

Now, take the square root of this value:

√(0.62758724) ≈ 0.793

Next, calculate 3a:

3a = 3 × 0.1039 = 0.3117

Now, add the results:

√(4a² - 4a + 1) + 3a = 0.793 + 0.3117 = 1.1047

Rounding to four decimal places, we get:

1.1047 ≈ 1.1039

So, the correct answer is:

c) 1.1039