# How do you simplify sqrt(16b)^4?

Apr 7, 2015
• $\sqrt{16 \cdot {b}^{4}}$ = $\pm 4 {b}^{2}$

• We use the Identity $\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$

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

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

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

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

• Squaring $4 \cdot {b}^{2}$ will give us $16 \cdot {b}^{4}$. And squaring $- \left(4 \cdot {b}^{2}\right)$ will also give us $16 \cdot {b}^{4}$

Hence $\sqrt{16 \cdot {b}^{4}}$ = $\pm 4 {b}^{2}$