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CTET Paper II (Mathematics and Science) Sep 2016 Solved Paper

Question : 41 of 150

Marks: +1, -0

\frac{\sqrt{1058}\times \sqrt{648}}{x}=18

, then the value of x is

Solution:

Concept:

Rewrite the square roots by factoring the numbers into perfect squares, then simplify the product to solve for

x

Explanation:

Factor each number under the square root:

1058 = 2 \times 529 = 2 \times 23^2

, so

\sqrt{1058} = 23\sqrt{2}

648 = 2 \times 324 = 2 \times 18^2

, so

\sqrt{648} = 18\sqrt{2}

Multiply:

\sqrt{1058} \times \sqrt{648} = (23 \times 18) \times (\sqrt{2} \times \sqrt{2}) = 414 \times 2 = 828

The equation becomes

\frac{828}{x} = 18

. Therefore,

x = \frac{828}{18} = 46

Answer:

D. 46

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