Could someone explain how to do these problems I have asked for help at school?

Question

But no one has tried to get back with me about these problems.
Multiply:
(2√[3] + √[6])(3√[3] – √[6])

Rationalize the denominator:
4____
√[7] – √[5]

Answer 1

For the first one, just use the FOIL method.

{{ FOIL = first, outside, inside, last }}

When you have something like (a+b)(c+d), you multiply the first terms in each parentheses (ac) then the outside (ad) then the inside (bc) then the last (bd) to get your answer.

So, using FOIL on your first problem we get:

(2√[3] + √[6]) (3√[3] – √[6]) =

{F} (2√[3] * 3√[3]) = 2*3*√[3]*√[3] = 2*3*3 = 18

{O} (2√[3] * –√[6]) = - 2√[3] * √[6] = - 2√[3] * √[3*2] = - 2√[3] * √[3] *√[2] = -2 * 3 * √[2] = -6√[2]

{I} √[6] * 3√[3] = √[3*2] * 3√[3] = √[3]*√[2] * 3√[3] = 3 * √[2] * 3 = 9√[2]

{L} √[6] * -√[6] = -6

Now add them all up:

18 - 6√[2] + 9√[2] - 6 =

12 + 3√[2]

HTH! :-)

Answer 2

(2√[3] + √[6])(3√[3] – √[6])

=2√[3])(3√[3] – √[6]) + √[6])(3√[3] – √[6])

= 2 * 3 * (√[9]) - 2 √[18] + 3√[18] - √[36])

= 18 + √[18] - 6
= 12 + √[9*2]
=12 + 3√[2]

4________
√[7] – √[5]

NOTE: (a + b)(a - b) = a² - b²
So (√[a] + √[b])([√a] - √b]) = a - b

So multiply numerator and denominator by √[7] + √[5] (These are called the irrational comjugates of each other for this reason)

So _____4____ x (√[7] + √[5])
....(√[7] – √[5]) x (√[7] + √[5])

= 4(√[7] + √[5])/(7 - 5)
= 2(√[7] + √[5])

Answer 3

(2√[3] + √[6])(3√[3] - √[6])
= 2√[3]*3√[3] - 2√[3]*√[6] + √[6]*3√[3] - √[6 ]*√[6]
= 6*3 - 2√[18] + 3√[18] -6
= 18 - 6 - √[18]
= 12 - √[18]
= 12 - √[2*9]
= 12 - √[2]*√[9]
= 12 - 3√[2]
= 3 (4 - √[2])

4/(√[7] - √[5])
multiply by (√[7] + √[5])/(√[7] + √[5])
then it becomes 4(√[7] + √[5])/ (7-5)
= 4/(7-5) * (√[7] + √[5])
= 4/2 * (√[7] + √[5])
=2 (√[7] + √[5])




/

Answer 4

Answer 1:
(2 root 3 + root 6)(3 root 3 + root 6)
= 2 root 3(3 root 3 + root 6) + root 6(3 root 3 + root 6)
= 18 + 6 root 2 + 9 root 2 + 6
= 24 + 15 root 2

Answer 2:
4/(root 7 - root 5)
Multiplying by conjugate
= [4/(root 7 - root 5)][(root 7 + root 5)/(root 7 + root 5)]
= [4(root 7 + root 5)/(root 7 - root 5)(root 7 + root 5)]
= (4 root 7 + 4 root 5)/7-5
= (4 root 7 + 4 root 5)/2
= 2 root 7 + 2 root 5

Answer 5

For the second one multiply top and bottom by √[7] + √[5]

Answer 6

1) It is the same as

(a+b)(c-d)= ac-ad+bc-bd

similarly

here it will be

2sqrt3*3sqrt3 - 2sqrt3*sqrt6+sqrt6*3sqrt3 - sqrt6*sqrt6
=> 6*3 - 2sqrt18 + 3sqrt18 - 6
=> 12+sqrt18
=> 12+3sqrt2

Thats the answer

Answer 7

try a scientific calculator