Write each mixed radical as an entire radical.−5𝑥 √6z

Question

Write each mixed radical as an entire radical.−5𝑥 √6z

Answer 1

To write the mixed radical −5𝑥 √6z as an entire radical, we can multiply the coefficient and the radical part together.

Starting with the coefficient, −5𝑥, we can rewrite it as −5 multiplied by 𝑥:

−5𝑥 √6z = -5√6z * 𝑥

So the entire radical form would be:

-5√6z * 𝑥

Answer 2

To write the mixed radical −5𝑥 √6𝑧 as an entire radical, we can combine the numeric and variable parts separately.

The given expression has two parts: −5𝑥 and √6𝑧.

1. Numeric part:
The numeric part of the expression is −5. Since there is no square root involved, it remains the same: −5.

2. Variable part:
The variable part of the expression is √6𝑧. To make it an entire radical, we need to simplify the square root.

√6 can be simplified as follows:
√6 = √(2 × 3) = √2 × √3 = √2√3.

Thus, the variable part becomes √2√3𝑧.

Combining the numeric and variable parts, the mixed radical −5𝑥 √6𝑧 can be rewritten as −5√2√3𝑧.

Answer 3

To write the given mixed radical as an entire radical, we need to simplify it.

The expression is −5𝑥√6z.

First, let's rearrange the terms to make it clear which parts of the expression are inside the square root.

I'll rewrite it as −5√(𝑥⋅6⋅𝑧).

Now, let's simplify:

−5√(𝑥⋅6⋅𝑧) = −5√(6𝑥𝑧).

To write this as an entire radical, we can multiply the constant, 6, by 𝑥 and 𝑧:

−5√(6𝑥𝑧) = −5√(6)√(𝑥𝑧).

Therefore, the entire radical form of −5𝑥√6𝑧 is −5√6√(𝑥𝑧).