Suppose that a and b are natural numbers. If 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><msqrt><mrow><mi>a</mi></mrow></msqrt><mo>+</mo><msqrt><mrow><mi>b</mi></mrow></msqrt></mrow></math> is
rational then show that 
it is a natural number. Show that, indeed both 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><msqrt><mrow><mi>a</mi></mrow></msqrt></mrow></math> and 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><msqrt><mrow><mi>b</mi></mrow></msqrt></mrow></math> are
then integers.  

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Suppose that a, b and c are natural numbers. If 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><msqrt><mrow><mi>a</mi></mrow></msqrt><mo>+</mo><msqrt><mrow><mi>b</mi></mrow></msqrt><mo>+</mo><msqrt><mrow><mi>c</mi></mrow></msqrt></mrow></math> is rational then show that it is a natural number. Moreover show
that 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><msqrt><mrow><mi>a</mi></mrow></msqrt></mrow></math> , 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><msqrt><mrow><mi>b</mi></mrow></msqrt></mrow></math> and 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><msqrt><mrow><mi>c</mi></mrow></msqrt></mrow></math> are then integers.

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