1. ## surd algebra help

express $\displaystyle \sqrt{22.5}$ in the form $\displaystyle K\sqrt{10}$

I dont get how to do this, can some one show me? Thanks.

2. Originally Posted by Tweety
express $\displaystyle \sqrt{22.5}$ in the form $\displaystyle K\sqrt{10}$

I dont get how to do this, can some one show me? Thanks.
Recall that
$\displaystyle \sqrt{ab} = \sqrt{a} \sqrt{b}$

$\displaystyle \sqrt{a^2} = a$

$\displaystyle \sqrt{22.5} = K\sqrt{10} = \sqrt{10K^2}$

Square both sides:

$\displaystyle 10K^2 = 22.5$

solve for K

3. $\displaystyle \sqrt{22.5} = \sqrt{2.25 \cdot 10} = \sqrt{2.25} \cdot \sqrt{10}$
So $\displaystyle K=\sqrt{2.25} = \frac{3}{2}$

4. Originally Posted by Tweety
express $\displaystyle \sqrt{22.5}$ in the form $\displaystyle K\sqrt{10}$

I dont get how to do this, can some one show me? Thanks.
Hi Tweety,

Another approach:

$\displaystyle \sqrt{22.5}=\sqrt{\frac{225}{10}}=15\sqrt{\frac{1} {10}}=\frac{15\sqrt{10}}{10}=\frac{3}{2}\sqrt{10}$

5. the correct answer is $\displaystyle \frac{3}{2}\sqrt{10}$
edit; oh right I get it now, thanks!

6. Originally Posted by Tweety
the correct answer is $\displaystyle \frac{3}{2}\sqrt{10}$
edit; oh right I get it now, thanks!
The square root of 2.25 is 1.5