# How do you simplify  sqrt( 32x^2) + sqrt( 50x^3) - sqrt( 18x^2)?

Apr 11, 2016

$\textcolor{b l u e}{\text{ } x \sqrt{2} \left(1 + 5 \sqrt{x}\right)}$. See explanantion

#### Explanation:

$\textcolor{b l u e}{\text{Assumption: "sqrt(50x^3)" is correct}}$

Note that $32 = {2}^{2} \times {2}^{2} \times 2$
$\text{ } 50 = {5}^{2} \times 2$
$\text{ } 18 = 2 \times 9 = 2 \times {3}^{2}$

Given:$\text{ } \sqrt{32 {x}^{2}} + \sqrt{50 {x}^{3}} - \sqrt{18 {x}^{2}}$

Write as:

""4xsqrt(2)+5xsqrt(2x)-3xsqrt(2)

""4xsqrt(2)+5xsqrt(2)sqrt(x)-3xsqrt(2)

Factor out $x \sqrt{2}$

$\textcolor{b l u e}{\text{ } x \sqrt{2} \left(4 + 5 \sqrt{x} - 3\right)}$
$\textcolor{b l u e}{\text{ } x \sqrt{2} \left(1 + 5 \sqrt{x}\right)}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Suppose: "sqrt(50x^3)" should be } \sqrt{50 {x}^{2}}}$

Proposed:$\text{ } \sqrt{32 {x}^{2}} + \sqrt{50 {x}^{2}} - \sqrt{18 {x}^{2}}$

Write as:

""4xsqrt(2)+5xsqrt(2)-3xsqrt(2)

$\textcolor{b l u e}{\implies 6 x \sqrt{2}}$