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Mathematics

The number which is to be subtracted from 72\sqrt{72} to get 32\sqrt{32} is:

  1. 2102\sqrt{10}

  2. 424\sqrt{2}

  3. 323\sqrt{2}

  4. 222\sqrt{2}

Rational Irrational Nos

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Answer

Let the number to be subtarcted be x.

⇒72−x=32⇒x=72−32⇒x=36×2−16×2⇒x=62−42⇒x=22.\Rightarrow \sqrt{72} - x = \sqrt{32} \\[1em] \Rightarrow x = \sqrt{72} - \sqrt{32} \\[1em] \Rightarrow x = \sqrt{36 \times 2} - \sqrt{16 \times 2} \\[1em] \Rightarrow x = 6\sqrt{2} - 4\sqrt{2} \\[1em] \Rightarrow x = 2\sqrt{2}.

Hence, Option 4 is the correct option.

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