Question

Proportion:

(2+√2)/(2-√2) = x/(3+√10)

Answer 1

\[(3 + \sqrt{10}) \dot\ \frac{2 + \sqrt{2}}{2 - \sqrt{2}}= x\]

Answer 2

Shouldn't we cross-multiply? With (3+√10) * (2+√2)?

Answer 3

That's the part that's confusing me.

Answer 4

Yes, you should

Answer 5

So, how did you get what you put above?

Answer 6

I Multiplied both sides by \(3 + \sqrt{10}\)

Answer 7

I'll try to show what I'm confused about...

Answer 8

This is what I thought it would be:

\[x = ((3+\sqrt{10})(2 + \sqrt{2}))/(2 - \sqrt{2})\]

So I don't get how we multiply both of (2+√2) / (2-√2) by (3+√10).

Answer 9

What you have is correct. You only multiply it with the numerator.

Answer 10

Oh okay...so how do we proceed/

Answer 11

Think of it this way

\[\frac{a}{b} \times \frac{c}{d} = \frac{ab}{cd}\]


So

\[\frac{3 + \sqrt{10}}{1} \dot\ \frac{2 + \sqrt{2}}{2 - \sqrt{2}}= \frac{(3 + \sqrt{10})(2 + \sqrt{2})}{2 - \sqrt{2}}\]

Answer 12

Yes, I get that.

Answer 13

To multiply \((3 + \sqrt{10})(2 + \sqrt{2})\) use the distributive property

Answer 14

So, would that be:

(6 + 3√2 + 2√10 + √20)?

Answer 15

Looks right

Answer 16

Alright, can you help me in dividing that by (2-√2)?

Answer 17

\[(6 + 3√2 + 2√10 + √20)\div (2-√2)\]

Answer 18

Hang on

Answer 19

Multiply the left side of the proportion by the conjugate first

\[\frac{(2+√2)}{(2-√2)} \times \frac{2 + \sqrt{2}}{2 + \sqrt{2}} = \frac{x}{(3+√10)}\]

Answer 20

Then simplify

Answer 21

Would that be 3 = x/(3x + √10)?

Answer 22

You have to multiply it all out properly.

Answer 23

Use FOIL to multiply if you have to

Answer 24

I'm getting 1 now, if I did it correctly.

Answer 25

No, you did not do it correctly. Post your steps here so I can point out what you are doing wrong.

Answer 26

(2 + √2)(2 + √2)
4 + 2√2 + 2√2 + √4
4 + 4√2 + 2
6 + 4√2

(2 - √2)(2 + √2)
4 + 2√2 - 2√2 - √4
4 - 2 = 2

(6 + 4√2)/2

Answer 27

That's better, but you're not done simplifying

Answer 28

Would it be 3 + 2√2?

Answer 29

Yes, now multiply both sides by \(3 + \sqrt{10}\) to isolate \(x\)

Answer 30

(3 + √10)(3 + 2√2)
9 + 6√2 + 3√10 + 2√20

Answer 31

Yes, but now you have to simplify \(2\sqrt{20}\)

Answer 32

9 + 6√2 + 3√10 + 2√20
2√ 4 * 5
4√5
9 + 6√2 + 3√10 + 4√5

Answer 33

Congrats

Answer 34

Thank you so much!

Answer 35

yw