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Powers and Roots Practice Test 3

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Question : 15 of 40

Marks: +1, -0

Simplify:

\sqrt{[(13.8)^2 - (12.8)^2] \div [(0.04)^2 + (0.04)(26.56)]}

$\sqrt{5}$
$\sqrt{6}$
5
-5
6

Solution:

Concept:

Use the difference of squares identity and factor the denominator.

Explanation:

Numerator:

(13.8)^2-(12.8)^2=(13.8+12.8)(13.8-12.8)=26.6 \times 1=26.6

.

Denominator:

(0.04)^2+(0.04)(26.56)=0.04(0.04+26.56)=0.04 \times 26.6

.

So the fraction becomes

\frac{26.6}{0.04 \times 26.6}=\frac{1}{0.04}=25

.

Taking the positive square root gives

\sqrt{25}=5

.

Answer:

5

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