Question

how do i solve this problem?

Answer 1

Answer:

4b²

Step-by-step explanation:

We are evaluating the square root:

$\sqrt{16b^4$

First, we can rewrite the square root of a product as the product of the square roots of its factors. In equation form:

$\sqrt{a\cdot b} = \sqrt a \cdot \sqrt b$

↓↓↓

$\sqrt{16b^4}=\sqrt{16} \cdot \sqrt{b^4}$

Next, we can evaluate the square root of 16:

$\sqrt{16} = \sqrt{4\cdot 4} = 4$

↓↓↓

$\sqrt{16}\cdot \sqrt{b^4}=4 \cdot \sqrt{b^4}$

And finally, we can evaluate the square root of b⁴ by splitting it into two b²'s:

$4 \cdot \sqrt{b^4} = 4\sqrt{b^2 \cdot b^2} = \boxed{4b^2}$