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2sqrt162

2162 2 \sqrt{162}

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Full solution

Q. 2162 2 \sqrt{162}
  1. Factorize 162162: Apply the prime factorization method to simplify 162\sqrt{162}. 162162 can be factored into 2×812 \times 81, and 8181 is a perfect square (9×99 \times 9). So, 162\sqrt{162} can be written as 2×9×9\sqrt{2 \times 9 \times 9}.
  2. Separate perfect square: Separate the perfect square from the non-perfect square inside the square root. 162=2×9×9=2×9×9\sqrt{162} = \sqrt{2 \times 9 \times 9} = \sqrt{2} \times \sqrt{9 \times 9}.
  3. Simplify perfect square: Simplify the square root of the perfect square. 9×9=81=9\sqrt{9 \times 9} = \sqrt{81} = 9.
  4. Combine simplified roots: Combine the simplified square root with the remaining part. 162=2×9=92\sqrt{162} = \sqrt{2} \times 9 = 9\sqrt{2}.
  5. Multiply by coefficient: Multiply the simplified square root by the coefficient outside the radical.\newline2162=2×92=1822\sqrt{162} = 2 \times 9\sqrt{2} = 18\sqrt{2}.

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