How can I simplify √3 (√6 - 2√3) and also √1/2 · (√8 + √2)

Please try and explain this to me, I'm stuck.

Question 1)

Expand the brackets using the distributive property:

√18 - 2(3)
= √18 - 6

To simplify √18, think of two numbers that when multiplied together give 18 and one of those numbers needs to be a perfect square:

√9 x √2
= 3 x √2
= 3√2

= 3√2 - 6
-----------------
Question 2)

Simplify the radicals inside the brackets:

1 / (√2) [2√2 + √2]

Combine the radicals into a single radical:

1 / (√2) [3√2]

Rationalise the denominator by multiplying both the numerator and denominator by √2:

(√2) / 2 [3√2]

Expand the brackets:

3(2) / 2

= 3

√3 (√6 - 2√3) = √3* √6 - √3* 2 √3 because of the distributive property

√3* √6- √3*2 √3= 3 √2 - 6 because

√3* √3= √3^2 and since square root and squares cancel u get 3

And

√3* √6= √3* √3* √2 and we know that √3 * √3= 3 so you get √3* √6= 3 √2

Your answer is 3 √2 - 6


Now number 2

√1/2 * ( √8+ √2) remember the distrubutive property so it becomes √1/2* √8 + √1/2* √2
Whiich when you simplified u get √4+ √1 which is equal to 2+1 which is equal to 3.

first one:
sqrt(3.6) - 2.sqrt(3.3)=
sqrt(3.3.2) - 2.sqrt(3.3)=
3. sqrt(2) - 2.3 =
3. sqrt(2) - 6 =
3(sqrt(2) - 2)

Just follow these steps with a pencil and it will make sense.
Same thing for the next one.
Just multiply 1/2 by the number inside each square root and in the first one you will get 4 while in the second you will get 1. So the result is going to be:

sqrt(4) + sqrt(1)= 2 + 1 = 3

3 (√6 - 2√3) and also √1/2 · (√8 + √2)?

1.
sqrt(18)-2(3)=3sqrt(2)-6

2.
sqrt(1/2)*(sqrt(8)+sqrt(2))
=2sqrt(2)*sqrt(1/2)+sqrt(2)*sqrt(1/2)
=2+1=3