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Simplify sqrt(20)

Mathematics

ScanSolve AI Answer

Answer

252\sqrt{5}

Step-by-step solution

5 steps

To simplify the expression 1420−820−10514\sqrt{20} - 8\sqrt{20} - 10\sqrt{5}, we first need to simplify the square roots.

  1. Simplify 20\sqrt{20}

    We can rewrite 20 as a product of a perfect square and another number: 20=4×520 = 4 \times 5.

    20=4×5=4×5=25\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}
  2. Substitute the simplified radical into the expression

    Replace 20\sqrt{20} with 252\sqrt{5} in the original expression:

    14(25)−8(25)−10514(2\sqrt{5}) - 8(2\sqrt{5}) - 10\sqrt{5}
  3. Perform the multiplications

    285−165−10528\sqrt{5} - 16\sqrt{5} - 10\sqrt{5}
  4. Combine the like terms

    Since all terms now have 5\sqrt{5}, we can combine their coefficients:

    (28−16−10)5(28 - 16 - 10)\sqrt{5}
  5. Calculate the coefficients

    (12−10)5(12 - 10)\sqrt{5} 252\sqrt{5}
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