How do you simplify the expression #8sqrt(5/4)+3sqrt20-10sqrt(1/5)#?

3 Answers

Answer:

#8sqrt5#

Explanation:

#8sqrt(5/4)#

#sqrt4= 2# so the fraction looks like #8sqrt5/2#.
The 8 and the 2 can cancel out which leads to #4sqrt5#

#3sqrt20#

#sqrt20 = 2sqrt5#. Then multiply it by 3 which makes #6sqrt5#.

Now the problem looks like this:

#4sqrt5 + 6sqrt5 - 10sqrt(1/5)#

For #10sqrt(1/5)#, we will rationalise the denominator because we cannot have a root as the denominator.

#sqrt(1/5)xxsqrt5 = sqrt5/5#

It is now #10sqrt5/5#

The 10 and the 5 cancel out leaving #2sqrt5#.

The problem is now like this:

#4sqrt5 + 6sqrt5 - 2sqrt5#

#=8sqrt5#

Tip: Dealing with these types of problems, break them into small chunks to make your life easier.

Apr 7, 2017

Answer:

#color(red)(=8sqrt5#

Explanation:

#8sqrt(5/4)+3sqrt20-10sqrt(1/5)#

#:.=8 sqrt5/sqrt4+3sqrt(2*2*5)-10sqrt1/sqrt5#

#color(red)(sqrt2*sqrt2=2#

#:.=8sqrt5/sqrt(2*2)+3*2sqrt5-10 1/sqrt5#

#:.=8sqrt5/2+6 sqrt5/1-10/sqrt5#

#:.=(8sqrt5*sqrt5+2sqrt5*6sqrt5-20)/(2sqrt5)#

#:.=(8*5+12*5-20)/(2sqrt5)#

#:.=(40+60-20)/(2sqrt5) #

#:.=80/(2sqrt5)#

#:.=40/sqrt5#

#:.=40/sqrt5 xx sqrt5/sqrt5# rationalise denominator

#:.(cancel40^color(red)8sqrt5)/cancel5^color(red)1#

#:.color(red)(8sqrt5#

Apr 9, 2017

Answer:

Slightly different approach

#8sqrt(5)#

Explanation:

Multiply by 1 and you do not change the value. But 1 comes in many forms. So you can change the way something looks without changing its intrinsic value.

Build a common factor by trying to have a #sqrt(5)# in all the numerators:

#color(green)([8sqrt(5/4)color(white)(.) ] + [3sqrt(20)] -[10sqrt(1/5)color(red)(xx1)]#

#color(green)([8sqrt(5/4)color(white)(.) ] + [3sqrt(20)] -[10sqrt(1/5)color(red)(xxsqrt(5)/sqrt(5)color(white)(.))]#

#color(green)([8(sqrt(5))/(sqrt(4))color(white)(.) ] + [3sqrt(4xx5)] -[10(sqrt(1))/(sqrt(5))color(red)(xxsqrt(5)/sqrt(5)color(white)(.))]#

#color(green)([4sqrt(5)color(white)(.)]color(white)(.) +color(white)(..) [6sqrt(5)color(white)(.)]color(white)(.)-" "[2sqrt(5)color(white)(.)]#

#sqrt(5)color(white)(.)(4+6-2)#

#8sqrt(5)#