Question

Simplify the square root (Picture provided)

Answer 1

For this case we must find the value of the following expression:

$\sqrt {8 ^ {17}}$

We have to:

$8 ^ {17} = 8 ^ 1 * 8 ^ {16}$

Substituting:

$\sqrt {8 * 8 ^ {16}}$

By definition of properties of powers and roots we have:

$\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}$

So:

$8 ^ {\frac {16} {2}} * \sqrt {8}\\8 ^ 8 * \sqrt {8}$

So we have to:

$\sqrt {8 ^ {17}} = 8 ^ 8 * \sqrt {8}$

Answer:

$8 ^ 8 * \sqrt {8}$

Option A