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SATMathematics Practice Test 1

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Question : 20 of 58

Marks: +1, -0

If

a = 5\sqrt{2}

2a = \sqrt{2x}

,what is the value of

x

?

Your Answer:

Solution:

Since

a = 5\sqrt{2}

,one can substitute

5\sqrt{2}

for

a

in

2a = \sqrt{2x}

,giving

10\sqrt{2} = \sqrt{2x}

,

Squaring each side of

10\sqrt{2} = \sqrt{2x}

gives

(10\sqrt{2})^2 = (\sqrt{2x})^2

,

which simplifies to

(10^2)(\sqrt{2})^2 = (\sqrt{2x})^2

,or

200 = 2x

.The gives

x = 100

.

Checking

x = 100

in the original equation gives

2(5\sqrt{2}) - \sqrt{(2)(100)}

,

which is true since

2(5\sqrt{2}) = 10\sqrt{2}

and

\sqrt{(2)(100)} = (\sqrt{2})(\sqrt{100}) = 10\sqrt{2}

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