How do you simplify 4sqrt18 - 7 sqrt72?

Aug 5, 2018

$\sqrt{18} = \sqrt{9} \sqrt{2} = 3 \sqrt{2}$

$\sqrt{72} = \sqrt{36} \sqrt{2} = 6 \sqrt{2}$

So $4 \sqrt{18} - 7 \sqrt{72} = 12 \sqrt{2} - 42 \sqrt{2} = - 30 \sqrt{2}$

Aug 6, 2018

$- 30 \sqrt{2}$

Explanation:

Since $72 = 4 \cdot 18$, we can rewrite $\sqrt{72}$ as $\sqrt{4} \sqrt{72}$. We now have

$4 \sqrt{18} - 7 \sqrt{4} \sqrt{18}$

This can be simplified further to

$4 \sqrt{18} - 14 \sqrt{18}$

Next, we can factor out a $\sqrt{18}$ to get

$\left(4 - 14\right) \sqrt{18} = - 10 \sqrt{18}$

Similar to how we simplified $\sqrt{72}$, we can simplify $\sqrt{18}$, rewriting it as $\sqrt{9} \sqrt{2}$. We now have

$- 10 \sqrt{9} \sqrt{2}$, which simplifies to

$- 30 \sqrt{2}$

Hope this helps!