Question

PLEASE ANSWER ASAP

Answer 1

Answer:

I've attached the Answer

Step-by-step explanation:

here it is

Answer 2

Answer:

$(\sqrt{6}+\sqrt{3})(\sqrt{6}-\sqrt{3})=3$

$(\sqrt{5}-\sqrt{2})(\sqrt{2}+\sqrt{5})=3$

Step-by-step explanation:

We want to simplify the expression:

$(\sqrt{6}+\sqrt{3})(\sqrt{6}-\sqrt{3})$

Notice that this is the difference of two squares pattern. Namely:

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

If we let a = √6 and b  =√3, we acquire:

$(a+b)(a-b)$

Expand accordingly:

$=a^2-b^2$

Back-substitute:

$=(\sqrt{6})^2-(\sqrt{3})^2$

Simplify:

$=6-3=3$

For the second expression, we have a similar pattern:

$(\sqrt{5}-\sqrt{2})(\sqrt{2}+\sqrt{5})$

We can first rewrite the expression (commutative property):

$=(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})$

And if we let a = √5 and b = √2:

$=(a-b)(a+b)$

Expand accordingly:

$=a^2-b^2$

Back-substitute and simplify:

$=(\sqrt{5})^2-(\sqrt{2})^2=5-2=3$