Question

What expression is equivalent to ^3 square root of 2y^3 times 7 square root of 18y

Answer 1

Answer:

$\sqrt[3]{2y^3} * 7\sqrt{18y} = 21(y^{\frac{3}{2}})(2^{\frac{5}{6}})$

Step-by-step explanation:

The question is poorly formatted.

Given

$\sqrt[3]{2y^3} * 7\sqrt{18y}$

Required

Derive an equivalent expression

$\sqrt[3]{2y^3} * 7\sqrt{18y}$

Express 18 as 9 * 2

$\sqrt[3]{2y^3} * 7\sqrt{9 * 2y}$

Split the expression as follows:

$\sqrt[3]{2y^3} * 7\sqrt{9} * \sqrt{2y}$

Take positive square root of 9

$\sqrt[3]{2y^3} * 7*3 * \sqrt{2y}$

$\sqrt[3]{2y^3} * 21 * \sqrt{2y}$

$21*\sqrt[3]{2y^3} * \sqrt{2y}$

The cube root can be rewritten to give:

$21*\sqrt[3]{2}*\sqrt[3]{y^3} * \sqrt{2y}$

$\sqrt[3]{y^3} = y^{3*\frac{1}{3}} = y$

So, we have:

$21*\sqrt[3]{2} * y * \sqrt{2y}$

Rewrite as:

$21y *\sqrt[3]{2} * \sqrt{2y}$

Split $\sqrt{2y$

$21y *\sqrt[3]{2} * \sqrt{2} * \sqrt{y}$

Collect Like Terms

$21y*\sqrt{y} *\sqrt[3]{2} * \sqrt{2}$

Represent in index form

$21y*y^{\frac{1}{2}} *2^\frac{1}{3} *2^\frac{1}{2}$

Apply law of indices

$21*y^{1+\frac{1}{2}} *2^{\frac{1}{3} +\frac{1}{2} }$

$21*y^{\frac{2+1}{2}} *2^{\frac{2+3}{6}}$

$21*y^{\frac{3}{2}} *2^{\frac{5}{6}}$

$21(y^{\frac{3}{2}})(2^{\frac{5}{6}})$

Hence:

$\sqrt[3]{2y^3} * 7\sqrt{18y} = 21(y^{\frac{3}{2}})(2^{\frac{5}{6}})$