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

3 Answers

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

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

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)