Simplify the following expression: \$\sqrt(8x^2 y) /\sqrt(2xy)\$.

The given expression is

\$\sqrt(8x^2 y) /\sqrt(2xy)\$

Combine the radicals under a single radical sign:

\$\sqrt((8x^2 y) / (2xy))\$

Simplify the fraction inside the radical and then divide the numerator and the denominator by the common factors 2 and xy:

\$ (8x^2 y) / (2xy)\$

\$ \cancel(8)^4 / \cancel(2) . \cancel(x^2)^x / \cancelx . \cancely /\cancely = 4x\$

Simplify the radical expression:

\$\sqrt(4x)\$

Since 4 is a perfect square, we can take the square root of 4outside the radical:

\$\sqrt(4) . sqrt(x) = 2\sqrt(x)\$

So, therefore the simplified expression is \$2\sqrt(x)\$.

However, as shown in the steps above, the inner radical contains 4x, which simplifies to \$2\sqrt(x)\$, not 2x

2x

Option B is correct because the simplified form of the expression is \$2\sqrt(x)\$

\$2\sqrt(x)\$

Option C is incorrect because it simplifies to 2 without considering the presence of x inside the square root

2

It suggests that the simplified expression should include a factor of x outside the square root and a factor of \$\sqrt(2)\$ inside the square root

\$x\sqrt(2)\$

Option

B

Can you summarize what you’ve understood in the above steps?