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Powers and Roots Practice Test 5

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Question : 18 of 31

Marks: +1, -0

\sqrt{(272)^2-(128)^2}=?

256
240
200
144

Solution:

Concept:

Use the identity

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

to simplify the expression under the square root.

Explanation:

Let

a=272

and

b=128

.

Then

\sqrt{a^2-b^2}=\sqrt{(a+b)(a-b)}

.

Substitute the values:

\sqrt{(272)^2-(128)^2}=\sqrt{(272+128)(272-128)}

=\sqrt{400\times 144}

=\sqrt{57600}

=240

.

Answer:

The value is

240

, so option B is correct.

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