Find x x

Algebra Level 2

x × 18 x × 20 = 12108 10 \large \sqrt{x \times 18} \sqrt{x \times 20} = 12108\sqrt{10}

Find the sum of all digits of x x


The answer is 11.

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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1 solution

Jerry McKenzie
Jan 8, 2018

x × 18 x × 20 = 12108 10 \sqrt{x\times18} \sqrt{x\times20}=12108\sqrt{10}

⇒ 360 x 2 = 12108 10 \Rightarrow \sqrt{360x^{2}}=12108\sqrt{10}

⇒ 36 x 2 ⋅ 10 = 12108 10 \Rightarrow \sqrt{36x^{2}\cdot 10}=12108\sqrt{10}

⇒ 6 x 10 = 12108 10 \Rightarrow 6x\sqrt{10}=12108\sqrt{10}

⇒ x = 12108 10 6 10 \Rightarrow x=\frac{12108\sqrt{10}}{6\sqrt{10}}

⇒ x = 2018 \Rightarrow x=2018

Thus the required answer is 2 + 0 + 1 + 8 = 11 2+0+1+8=11

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