Question

Which choices are equivalent to the expression below? Check all that apply.3 square root of 6A. sqrt 27 x sqrt 2B. sqrt 9x sqrt 6C. sqrt 27 x sqrt 4D. sqrt 54E. sqrt 18F. 54

Answer 1

the expression=

$3\sqrt[]{6}\text{ = 7,348}$

Like we did before, let's check first solving them

A. sqrt 27 x sqrt 2= 7,348 this one is correct

B. sqrt 9x sqrt 6= 7,348 this one is correct

C. sqrt 27 x sqrt 4= 10,39 no

D. sqrt 54= 7,348 this one is correct

E. sqrt 18= 4,24 no

F. 54 no

And now we apply properties to explain why they are the same expression

A=

$\sqrt[]{27}\cdot\sqrt[]{2}=\sqrt[]{27\cdot2}=\sqrt[]{54}=\sqrt[]{9\cdot6}=\sqrt[]{9}\cdot\sqrt[]{6}=3\cdot\sqrt[]{6}$

note= to the 9 x 6, what I did was divide 54 by the number on the sqrt on the expression (6)

B=

$\sqrt[]{9}\cdot\sqrt[]{6}=3\cdot\sqrt[]{6}$

and the last one

D=

$\sqrt[]{54}=\sqrt[]{9\cdot6}=\sqrt[]{9}\cdot\sqrt[]{6}=3\cdot\sqrt[]{6}$