12th Problem 2016

Algebra Level 3

Simplify:

50 x + 200 x + 288 x + 2738 x \sqrt { 50x } +\quad \sqrt { 200x } +\quad \sqrt { 288x } +\quad \sqrt { 2738x }

Check out the set: 2016 Problems

64 x 64\sqrt { x } 27 2 x + 2738 x 27\sqrt { 2x } +\sqrt { 2738x } 64 2 x 64\sqrt { 2x } 64 x 2 64x\sqrt { 2 }

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1 solution

Ashish Menon
Apr 21, 2016

50 x + 200 x + 288 x + 2738 x = 25 2 x + 10 2 x + 12 2 x + 37 2 x = 2 x ( 25 + 10 + 12 + 37 ) = 64 2 x \begin{aligned} \sqrt{50x} + \sqrt{200x} + \sqrt{288x} + \sqrt{2738x} & = 25\sqrt{2x} + 10\sqrt{2x} + 12\sqrt{2x} + 37\sqrt{2x}\\ \\ & = \sqrt{2x}(25 + 10 + 12 + 37)\\ \\ & = \boxed{64\sqrt{2x}} \end{aligned}

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