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Simplify the expression sqrt(5) into the form a+bsqrt(c) where a, b, and c are integers.

Mathematics

ScanSolve AI Answer

Answer

0+150 + 1\sqrt{5}

Step-by-step solution

3 steps
  1. Identify the given expression and the required form.

    The expression to simplify is 5\sqrt{5}.
    The required form is a+bca+b\sqrt{c}, where aa, bb, and cc are integers.

  2. Simplify the radical.

    The number 5 is a prime number, so it has no perfect square factors other than 1. Therefore, 5\sqrt{5} is already in its simplest radical form.

  3. Express the simplified radical in the required form a+bca+b\sqrt{c}.

    We can write 5\sqrt{5} as:

    0+150 + 1\sqrt{5}

    Comparing this to a+bca+b\sqrt{c}:
    a=0a = 0
    b=1b = 1
    c=5c = 5

    All aa, bb, and cc are integers.

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