Math question?

Question

1) (2x-1)^2 = 81 solve using square root property

2) rationalize 5/square root of 7 (conjugates where needed)

3) (2 square root of 2 - square root of 3)(2 square root of 2 + square root of 3) (using FOIL)

I have a test tomorrow and have the answers to these already, however I have no idea how to do them, so any help on these types are highly appreciated, thank you all.

thanks, i get how to do #2 now, the others not as clearly

thanks I get it now, but how does 2 square root of 2 X 2 square root of 2 = 8 ?

Answer 1

(2x - 1)² = 81

(√2x - 1)² = √81

2x - 1 = 9

2x - 1 + 1 = 9 + 1

2x - 10

2x / 2 = 10 / 2

x = 10/ 2

x = 5

- - - - - - -

5 / √7 =

5 √7 / √7 √7

5√7 / √49

5 √7 / 7

- - - - - - - -s-

Answer 2

1)
(2x-1)² = 81

2x-1 = ±√81

2x-1 = ±9

2x = 10 or 2x = -8

so x = 5 or x = -4.

2)

(5 /√7) *(√7 /√7) = (5 *√7) /(√7 *√7) = (5√7)/7

3)

(2√2 - √3)(2√2 + √3)

(2√2)² +2√2√3 - 2√2√3 - (√3)²

The middle terms cancel.

You get 4*2 - 3 = 5.

Answer 3

1) (2x-1)^2 = 81

(2x-1)^2 = 9^2

Taking square root on both sides,

2x -1 = 9

2x = 9 + 1

2x = 10

Dividing both sides by 2,

x = 5

2) 5/ square root of 7

on rationalizing, we get,

(5/square root of 7) x (square root of 7/square root of 7) = (5 square root of 7)/ 7

3) (2 square root of 2 - square root of 3) (2 square root of 2 + square root of 3)

FOIL method means First Out In Last

First ---> (2 square root of 2) x (2 square root of 2) = 8

OUT -----> (2 square root of 2) x (square root of 3) = 2 square root of 6

IN -----> -(square root of 3) x (2 square root of 2) = - 2 square root of 6

Last ----> -(square root of 3) x (square root of 3) = -3

Therefore, the answer is....

8 - 3 = 5 (because 2 square root of 6 and - 2 square root of 6 gets cancelled)

Answer 4

1.
(2x - 1)^2 = 81
Take square root:
2x - 1 = +/- 9
2x = 1 + 9 or 1 - 9
x = 10/2 or -8/2
= 5 or -4

2.
Multiply top and bottom by sqrt(7):
5sqrt(7) / sqrt(7)*sqrt(7)
= 5sqrt(7) / 7.

3.
( 2sqrt(2) - sqrt(3) ) ( 2sqrt(2) + sqrt(3) )
= 4*2 + 2sqrt(2)*sqrt(3) - 2sqrt(2)sqrt(3) - 3
= 8 - 3
= 5.

Answer 5

1) take square root on both sides
then add one on both sides
then divide by 2 on both sides

2) multiply the numerator and denominator by square root of 7