# How do you simplify sqrt(9-(9/2))?

May 4, 2016

$\frac{3 \sqrt{2}}{2}$

#### Explanation:

Consider the following: If you multiply a value by 1 you not change it value$\text{ } 6 \times 1 = 6$. However, 1 comes in many forms. One of them is $1 = \frac{2}{2} \text{ }$ Multiplying by this does not change the value but it does change the way it looks.
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$\textcolor{b l u e}{\text{Answering the question}}$

Multiply the 9 by 1 but in the form of $1 = \frac{2}{2}$

write as:$\text{ } \sqrt{\left(9 \times \frac{2}{2}\right) - \frac{9}{2}}$

$\sqrt{\frac{18}{2} - \frac{9}{2}} \text{ "=" } \sqrt{\frac{9}{2}}$

Write as: $\text{ "sqrt(9)/sqrt(2)" "=" } \frac{3}{\sqrt{2}}$

But it is not good practice to have a root as a denominator

Multiply by 1 but in the form of $1 = \frac{\sqrt{2}}{\sqrt{2}}$

Giving:$\text{ } \frac{3}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}$

$= \frac{3 \sqrt{2}}{2}$