# How do you multiply sqrt[27b] * sqrt[3b^2L]?

Jun 25, 2017

$\sqrt{27 b} \cdot \sqrt{3 {b}^{2} L} = 9 b \sqrt{b L}$

#### Explanation:

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

Therefore $\sqrt{27 b} \cdot \sqrt{3 {b}^{2} L}$

= $\sqrt{27 b \times 3 {b}^{2} L}$

= $\sqrt{3 \times 3 \times 3 \times \textcolor{red}{b \times 3} \times b \times b \times L}$

= $\sqrt{3 \times 3 \times 3 \times \textcolor{red}{3 \times b} \times b \times b \times L}$

= $\sqrt{\underline{3 \times 3} \times \underline{3 \times 3} \times \underline{b \times b} \times b \times L}$

= $3 \times 3 \times b \times \sqrt{b L}$

= $9 b \sqrt{b L}$

Jun 25, 2017

color(blue)(9bsqrt(bL)

#### Explanation:

$\sqrt{27 b} \cdot \sqrt{3 {b}^{2} L}$

$\therefore = \sqrt{3 \cdot 3 \cdot 3 b} \cdot \sqrt{3 {b}^{2} L}$

$\therefore = 3 \sqrt{3 b} \cdot \sqrt{3 {b}^{2} L}$

$\therefore = 3 \sqrt{3 b} \cdot b \sqrt{3 L}$

$\therefore = 3 b \sqrt{3 b 3 L}$

$\therefore = 3 \cdot 3 b \sqrt{b L}$

:.color(blue)(=9bsqrt(bL)