# Thread: square roots

1. ## square roots

hi

can you help me to resolve a square root task?
i have marked square roots with S-letters.
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1 / S3 * ( S3 + 3 / S2 * S3 ) * S2

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cecilia

2. Originally Posted by Cecilia6
hi

can you help me to resolve a square root task?
i have marked square roots with S-letters.
_____________________________________________

1 / S3 * ( S3 + 3 / S2 * S3 ) * S2

_____________________________________________

cecilia
Do you mean:

$\displaystyle \dfrac1{\sqrt{3} \cdot \left( \sqrt{3} + \frac3{\sqrt{2} \cdot \sqrt{3}} \right) \cdot \sqrt{2}}$

If so: Expand the bracket in the denominator:

$\displaystyle \dfrac1{3 \cdot \sqrt{2}+3}=\dfrac1{3(\sqrt{2} + 1)} = \dfrac{\sqrt{2}-1}3$

3. no, that's not what i meant it's difficult to mark it better than i did it, because i don't know how to type the right marks

4. ## Square Roots

Hello Cecilia6
Originally Posted by Cecilia6
hi

can you help me to resolve a square root task?
i have marked square roots with S-letters.
_____________________________________________

1 / S3 * ( S3 + 3 / S2 * S3 ) * S2

_____________________________________________

cecilia
Let me have another guess then! Perhaps you mean

$\displaystyle \frac{1}{\sqrt{3}} \times \left(\sqrt{3} + \frac{3}{\sqrt {2} \sqrt{3}}\right) \times \sqrt{2}$

If that's it, then you can simplify it like this:

$\displaystyle \frac{1}{\sqrt{3}} \times \left(\sqrt{3} + \frac{3}{\sqrt {2} \sqrt{3}}\right) \times \sqrt{2}$

$\displaystyle = \frac{\sqrt{2}}{\sqrt{3}}\times \frac{\sqrt{3}\sqrt{2}\sqrt{3}+3}{\sqrt{2}\sqrt{3} }$

$\displaystyle = \frac{\sqrt{2}}{\sqrt{3}}\times \frac{3\sqrt{2}+3}{\sqrt{2}\sqrt{3}}$

$\displaystyle = \frac{\sqrt{2}\times 3(\sqrt{2}+1)}{3\sqrt{2}}$

$\displaystyle = \sqrt{2} + 1$

5. Hello, Cecilia!

Knowing the way the inexperienced expresses division,
. . I think I know what the problem says.

$\displaystyle \frac{1}{\sqrt{3}}\left(\frac{\sqrt{3} + 3}{\sqrt{2}\cdot\sqrt{3}}\right)\sqrt{2}$

We can reduce immediately: .$\displaystyle \frac{1}{\sqrt{3}}\left(\frac{\sqrt{3}+3}{{\color{ red}\rlap{///}}\sqrt{2}\cdot\sqrt{3}}\right){\color{red}\rlap{///}}\sqrt{2}$

. . . $\displaystyle =\;\frac{1}{\sqrt{3}}\left(\frac{\sqrt{3}+3}{\sqrt {3}}\right) \;= \;\frac{\sqrt{3}+3}{\sqrt{3}\cdot\sqrt{3}} \;=\;\frac{\sqrt{3}+3}{3}$