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

Question

Gabriel Agustin · Accepted Answer

#sqrt(27b)*sqrt(3b^2L)=9bsqrt(bL)# As #sqrta*sqrtb=sqrt(axxb)# Therefore #sqrt(27b)*sqrt(3b^2L)# = #sqrt(27bxx3b^2L)# = #sqrt(3xx3xx3xxcolor(red)(bxx3)xxbxxbxxL)# = #sqrt(3xx3xx3xxcolor(red)(3xxb)xxbxxbxxL)# = #sqrt(ul(3xx3)xxul(3xx3)xxul(bxxb)xxbxxL)# = #3xx3xxbxxsqrt(bL)# = #9bsqrt(bL)#

Zoe Adams · Answer

#color(blue)(9bsqrt(bL)# #sqrt(27b)*sqrt(3b^2L)# #:.=sqrt(3*3*3b)*sqrt(3b^2L)# #:.=3sqrt(3b)*sqrt(3b^2L)# #:.=3sqrt(3b)*bsqrt(3L)# #:.=3bsqrt(3b3L)# #:.=3*3bsqrt(bL)# #:.color(blue)(=9bsqrt(bL)#

Julian Avila · Answer

undefined To multiply $\sqrt{27b}$ by $\sqrt{3b^2L}$, you can first simplify each square root individually:

1. $\sqrt{27b} = \sqrt{9 \times 3 \times b} = \sqrt{9} \times \sqrt{3} \times \sqrt{b} = 3\sqrt{3b}$
2. $\sqrt{3b^2L} = \sqrt{3 \times b \times b \times L} = \sqrt{3} \times \sqrt{b} \times \sqrt{b} \times \sqrt{L} = b\sqrt{3L}$

Then, multiply the simplified expressions together:

$$3\sqrt{3b} \times b\sqrt{3L} = 3b \times \sqrt{3b} \times \sqrt{3L} = 3b \times \sqrt{(3b)(3L)} = 3b\sqrt{9bL} = 3b \times 3\sqrt{bL} = 9b\sqrt{bL}$$

So, the product of $\sqrt{27b}$ and $\sqrt{3b^2L}$ is $9b\sqrt{bL}$.