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Rationalize the denominator of the expression 1+sqrt(2)sqrt(2).

Mathematics

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Answer

2+22\mathbf{\frac{\sqrt{2} + 2}{2}}

Step-by-step solution

3 steps

Here's the solution for 2a.i:

  1. Identify the expression to rationalize.

    The expression is 1+22\frac{1+\sqrt{2}}{\sqrt{2}}. To rationalize the denominator, we need to eliminate the square root from the denominator.

  2. Multiply the numerator and denominator by 2\sqrt{2}.

    1+22×22\frac{1+\sqrt{2}}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}

  3. Distribute and simplify the numerator and denominator.

    =(1)(2)+(2)(2)(2)(2)= \frac{(1)(\sqrt{2}) + (\sqrt{2})(\sqrt{2})}{(\sqrt{2})(\sqrt{2})} =2+22= \frac{\sqrt{2} + 2}{2}

    The simplified expression is:

    2+22\mathbf{\frac{\sqrt{2} + 2}{2}}
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