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Math Help - Squaring a radical

  1. #1
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    Squaring a radical

    When plugging in the area of a circle formula, I ran into something I can't figure out.

    Lets say that the radius is (5 sqr root of 2/2) Its a fraction. When plugging it into the formula, it becomes (5 sqr root of 2/2)^2. I know the correct answer is 25/2, however, that is what I am not understanding.

    Please clarify for me: Pretending that it is not in fraction form, 5 sqr root of 2 * 5 sqr root of 2 would equal 50, correct?

    It becomes 25 * 2= 50, correct?
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  2. #2
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    Re: Squaring a radical

    If you think about this as (5 squared) times ((sq. root of 2) squared) and then all divided by (2 squared) and did each piece separately you would get 25 times 2 or (50) and that would be divided by 4 and you would end up with 25/2.
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  3. #3
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    Re: Squaring a radical

    Quote Originally Posted by KingNathan View Post
    When plugging in the area of a circle formula, I ran into something I can't figure out.

    Lets say that the radius is (5 sqr root of 2/2) Its a fraction. When plugging it into the formula, it becomes (5 sqr root of 2/2)^2. I know the correct answer is 25/2, however, that is what I am not understanding.

    Please clarify for me: Pretending that it is not in fraction form, 5 sqr root of 2 * 5 sqr root of 2 would equal 50, correct?

    It becomes 25 * 2= 50, correct?
    \displaystyle \begin{align*}\left(\frac{5\sqrt{2}}{2}\right)^2 &= \frac{5^2 (\sqrt{2})^2}{2^2} \\ &= \frac{25\cdot 2}{4} \\ &= \frac{25}{2} \end{align*}
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  4. #4
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    Re: Squaring a radical

    Quote Originally Posted by KingNathan View Post
    Lets say that the radius is (5 sqr root of 2/2) Its a fraction. When plugging it into the formula, it becomes (5 sqr root of 2/2)^2. I know the correct answer is 25/2, however, that is what I am not understanding.
    Let's keep it simple; your problem is simply lack of brackets:
    your (5 sqr root of 2/2)^2 should be: [(5 sqr root of 2) / 2]^2
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