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Powers and Roots Practice Test 5

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Question : 6 of 31

Marks: +1, -0

What is the square root of

\frac{(0.84)^3}{1-0.84}+[0.84+(0.84)^2+1]

?

6.25
7.5
3.5
2.5
15.1

Solution:

Concept:

The expression can be simplified using the identity

(1-a)(a^2+a+1)=1-a^3

.

Explanation:

Let

a=0.84

.

The expression inside the square root is

\frac{a^3}{1-a}+(a+a^2+1)

.

Take

1-a

as the common denominator:

\frac{a^3+(1-a)(a^2+a+1)}{1-a}

Using

(1-a)(a^2+a+1)=1-a^3

, the numerator becomes:

a^3+1-a^3=1

So the expression becomes:

\sqrt{\frac{1}{1-0.84}}=\sqrt{\frac{1}{0.16}}=\sqrt{\frac{100}{16}}=\frac{10}{4}=2.5

Answer:

2.5

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