Question

Which expression is equivalent to sqrt8x^7y^8? assume x>0

Answer 1

Answer:

$\sqrt{8x^7y^8$$= 2x^3y^4 * \sqrt{2x}$

Step-by-step explanation:

Given

$\sqrt{8x^7y^8$

Required

Evaluate

$\sqrt{8x^7y^8$

Separate each factor with multiplication sign

$\sqrt{8*x^7*y^8$

Express 8 as 4 * 2 and $x^7$ as $x^6 * x$

$\sqrt{4 * 2 *x^6 * x*y^8$

Split each factor

$\sqrt{4} * \sqrt{2} *\sqrt{x^6} * \sqrt{x}*\sqrt{y^8}$

Evaluate $\sqrt4$

$2 * \sqrt{2} *\sqrt{x^6} * \sqrt{x}*\sqrt{y^8}$

Apply law of indices:

$2 * \sqrt{2} * x^{6*\frac{1}{2}} * \sqrt{x} * y^{8*\frac{1}{2}}$

$2 * \sqrt{2} * x^3 * \sqrt{x} * y^4$

Reorder

$2* x^3 * y^4 * \sqrt{2} * \sqrt{x}$

$2x^3y^4 * \sqrt{2} * \sqrt{x}$

$2x^3y^4 * \sqrt{2*x}$

$2x^3y^4 * \sqrt{2x}$

$2x^3y^4 \sqrt {2x$

Hence:

$\sqrt{8x^7y^8$$= 2x^3y^4 * \sqrt{2x}$

Answer 2

Answer: It is C or 2x^3y^4 square root2x.

Step-by-step explanation: Checked on my calculator it is correct.