# how do u solve: 1. (2√2-1)/(2√2)? 2. (3√2+2√3)/(2√5-5√2)? been trying all nite pls?!

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1. 2sqrt(2)-1/ 2sqrt2

First multiply bu sqrt(2)

==> [2sqrt(2)*sqrt2 - 1*sqrt2]/2sqrt2*sqrt2

==> (2*2 -sqrt2)/2*2

==> (4-sqrt2)/4

==> 1-sqrt2/4

2. 3sqrt2 +2sqrt3/(2sqrt5-5sqrt2)

Let us multiply by 2sqrt5+5sqrt2

==> (3sqrt2+2sqrt3)(2sqrt5+5sqrt2)/ (2sqrt5-5sqrt2)(2sqrt5+5sqrt2)

==> 6sqrt10 + 4sqrt15 + 15*2 + 10sqrt6 / 4*5 - 25*2

==> 30 + 6sqrt10 + 4sqrt15 +10 sqrt6 / 20 - 50

==> -1 + (-1/5)sqrt10 + (-2/15)sqrt15 + (-1/3)sqrt6

1) For the first issue, you can write the ratio in this way:

(2√2-1)/(2√2) = (2√2)/(2√2) - 1/(2√2)

It is easy to notice that (2√2)/(2√2) = 1.

So, the expression will be written as:

1 - 1/(2√2)

Now, we'll rationalise 1/(2√2), by multiplying both, numerator and denominator by √2.

1/(2√2) = √2/2*√2*√2 = √2/2*2 = √2/4

The expression is:

1 - 1/(2√2) =1 - √2/4

2) (3√2+2√3)/(2√5-5√2)

First thing for this ratio is that we are not allowed to let the denominator of the ratio to contain squares. For this reason, we'll multiply the denominator, also the numerator, by denominator's conjugate, which is 2√5+5√2. We'll get:

(3√2+2√3)*(2√5+5√2)/(2√5-5√2)(2√5+5√2)

We'll open the brackets and we'll get:

- the expression from numerator:

6*√2*√5+15*√2*√2+4*√3*√5+10*√3*√2 = 6√10+15*4+4*√15+10*√6

- the expression from denominator:

Being a difference of squares, we'll have the formula:

(a-b)(a+b) = a^2 - b^2

(2√5-5√2)(2√5+5√2) = (2√5)^2 - (5√2)^2

(2√5-5√2)(2√5+5√2) = 4*5 - 25*2 = 20-50 = -30

The expression will become:

(6√10+60+4*√15+10*√6)/-30

1.

To simplify (2*sqrt2-1)/(2sqrt2).

Multiply both denominator and numerator by sqrt2 and rationalise the denominator:

2(sqrt2-1)(sqrt2)/(2(sqrt2)^2)

= (2*2-sqrt2/4

= 1 - (sqrt2)/4

2)

To simplify (3√2+2√3)/(2√5-5√2)

Deminator is 2sqrt5 -5sqrt. We multiply by 2sqrt5+5sqrt2 both denominator and numerator to rationalise the denominator.

(3sqr2+2sqrt3)(2sqrt5+5sqrt2)/ {(2sqrt5)^2-5sqrt2()^2)}

(6sqrt10 + 15*2 +4sqrt15+10sqrt6)/(20-50)

=(30+6sqrt15+4sqrt15+10sqrt6)/(-30)

=-(1+(1/5)sqrt10 + (2/15)sqrt15 +(1/3)sqrt6)