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Math Help - area of a square

  1. #1
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    area of a square

    i am i right in thinking that this area of a square-untitled1.jpgwould = area of a square-untitled2.jpg
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  2. #2
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    Quote Originally Posted by andyboy179 View Post
    i am i right in thinking that this Click image for larger version. 

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ID:	14854would = Click image for larger version. 

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ID:	14855
    Nope, the area is the product of the two sides

    A = \sqrt{5}(2+\sqrt{10}) = 2\sqrt{5} + 5\sqrt{2}


    In case you were wondering about the last term:

    \sqrt{5}\sqrt{10} = \sqrt{50} = \sqrt{25}\sqrt{2} = 5\sqrt{2}

    Alternatively

    \sqrt{5}\sqrt{10} = \sqrt{5}\sqrt{5}\sqrt{2} = 5\sqrt{2}
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  3. #3
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    Quote Originally Posted by e^(i*pi) View Post
    Nope, the area is the product of the two sides

    A = \sqrt{5}(2+\sqrt{10}) = 2\sqrt{5} + 5\sqrt{2}


    In case you were wondering about the last term:

    \sqrt{5}\sqrt{10} = \sqrt{50} = \sqrt{25}\sqrt{2} = 5\sqrt{2}

    Alternatively

    \sqrt{5}\sqrt{10} = \sqrt{5}\sqrt{5}\sqrt{2} = 5\sqrt{2}
    how did you work out A = \sqrt{5}(2+\sqrt{10}) = 2\sqrt{5} + 5\sqrt{2}?
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  4. #4
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    ..., could you explain it in more detail please?!?!?
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  5. #5
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    sorry, i'm confusing myself i think. so 2\sqrt{5} + 5\sqrt{2} is the answer?
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    Quote Originally Posted by andyboy179 View Post
    sorry, i'm confusing myself i think. so 2\sqrt{5} + 5\sqrt{2} is the answer?
    Yeah that's right.

    To solve it I used the fact that the area of a rectangle is length \times width and I also used the distributive property which says a(b+c) = ab+ac

    As the sides are 2+\sqrt{10} and \sqrt{5} to find the area I multiplied them.

    Surds act like any other number when multiplied and using the distributive property above for this case: a = \sqrt{5} and b= 2 and c=\sqrt{10}

    Therefore the area is ab+ac = 2\sqrt{5} + \sqrt{5}\sqrt{10}

    As a law of surds, for positive p,q: \sqrt{p}\sqrt{q} = \sqrt{pq} and so \sqrt{5}\sqrt{10} = \sqrt{50}

    You could leave the answer as 2\sqrt{5}+\sqrt{50} but it is more usual to simplify.

    To simplify a surd get the prime factors of the number inside it- in this case 50.

    50 = 2 \times 5 \times 5

    Using the rule directly above \sqrt{50} = \sqrt{2}\sqrt{5}\sqrt{5}

    because \sqrt{a}\sqrt{a} = a we can simplify the above to give \sqrt{2}\sqrt{5}\sqrt{5} = 5\sqrt{2} which is fully simplified.

    I then combined this with the first part (ab) and got the final answer of

    A = 2\sqrt{5}+5\sqrt{2}
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