Exercise 58 Page 372

Before multiplying the given radical expressions, we need to answer two questions.

The rule regarding multiplying radical expressions states that if

n a

and

n b

n a \cdot n b

=

n a b .

34 \cdot 380 = 3 4 \cdot 80

Because both radicals are real numbers and we can see that the given expressions have the same index, we can multiply them. Additionally,

4

and

80

are positive numbers, so we do not need to add any absolute value symbols.

34 \cdot 380

$3 a \cdot 3 b = 3 a \cdot b$

3 4 \cdot 80

3320

Next, let's simplify the radical expression by finding all of the perfect cubes inside the radical.

3320

Split into factors

3 64 \cdot 5

Write as a power

3 4^{3} \cdot 5

$3 a \cdot b = 3 a \cdot 3 b$

3 4^{3} \cdot 35

$n a^{n} = a$

4 \cdot 35

435