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Powers and Roots Practice Test 4

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Question : 1 of 40

Marks: +1, -0

The value of

\frac{0.08 \times 0.08 \times 0.08 + 0.02 \times 0.02 \times 0.02}{0.08 \times 0.08 - 0.0016 + 0.02 \times 0.02}

is simplified to:

0.001
0.1
.0016
.016

Solution:

Concept:

Use the sum of cubes identity

a^3+b^3=(a+b)(a^2-ab+b^2)

.

Explanation:

Let

a=0.08

and

b=0.02

.

Then

0.0016 = 0.08 \times 0.02 = ab

.

The given expression becomes

\frac{a^3+b^3}{a^2-ab+b^2}

.

Apply the identity:

a^3+b^3=(a+b)(a^2-ab+b^2)

.

Cancel the common factor

a^2-ab+b^2

.

So the expression simplifies to

a+b

.

Substitute back:

a+b=0.08+0.02=0.10

.

Answer:

0.1

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