# How do you divide 5sqrt(16y^4) + 7sqrt(2y)?

Aug 6, 2018

$\text{ }$
color(red)(5sqrt(16y^4) + 7sqrt(2y)=20y^2+7sqrt(2)sqrt(y)

#### Explanation:

$\text{ }$
Given: color(red)(5sqrt(16y^4) + 7sqrt(2y)

My understanding of the question: Simplify the radical expression.

$\Rightarrow \left(5\right) \left(\sqrt{16}\right) \sqrt{{y}^{4}} + 7 \sqrt{2} \sqrt{y}$

$\Rightarrow 5 \cdot 4 \cdot {y}^{2} + 7 \sqrt{2} \sqrt{y}$

$\Rightarrow 20 {y}^{2} + 7 \sqrt{2} \sqrt{y}$

You can stop here.

If you so wish, you can simplify in a different way.

Consider the step:

$\Rightarrow \left(5\right) \left(\sqrt{16}\right) \sqrt{{y}^{4}} + 7 \sqrt{2} \sqrt{y}$

$\Rightarrow \left(5\right) \left(\sqrt{16}\right) \sqrt{{y}^{3}} \sqrt{y} + 7 \sqrt{2} \sqrt{y}$

$\Rightarrow 5 \cdot 4 \cdot \sqrt{{y}^{3}} \sqrt{y} + 7 \sqrt{2} \sqrt{y}$

$\Rightarrow \sqrt{y} \left[20 \sqrt{{y}^{3}} + 7 \sqrt{2}\right]$

Hope this helps.

Aug 13, 2018

color(magenta)(=> (40/7) (y)^(3/2)

#### Explanation:

I am taking the sum as

$\frac{5 \cdot \sqrt{16 {y}^{4}}}{7 \sqrt{2 y}}$

as it has been asked to divide.

=> (5 * sqrt (2^4y^4)) / ( 7 sqrt (2y)

$\implies \left(\frac{5}{7}\right) \cdot \frac{\sqrt{{2}^{4} {y}^{4}}}{\sqrt{2} y}$

$\implies \left(\frac{5}{7}\right) \cdot \sqrt{{2}^{3} {y}^{3}}$

$\implies \left(\frac{40}{7}\right) {\left(y\right)}^{\frac{3}{2}}$