How do you simplify # 4sqrt48#?

2 Answers
Mar 6, 2018

Answer:

See a solution process below:

Explanation:

First, rewrite the expression as:

#4sqrt(16 * 3)#

Then use this rule for exponents to simplify the radical:

#sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))#

#4sqrt(color(red)(16) * color(blue)(3)) =>#

#4 * sqrt(color(red)(16)) * sqrt(color(blue)(3)) =>#

#4 * 4 * sqrt(color(blue)(3)) =>#

#16sqrt(3)#

Mar 6, 2018

Answer:

#4sqrt48=color(blue)(16sqrt3#

Explanation:

Simplify:

#4sqrt48#

Prime factorize #48#.

#4sqrt(2*2*2*2*3)#

#4sqrt(2^2*2^2*3)#

Apply rule: #sqrt(x^2)=x#

#4*2*2sqrt3#

Simplify.

#16sqrt3#