Why doesn't this (2root5)^2 simplify properly when I expand the brackets?

When I do it as (2 root 5)(2 root 5) because the bracket is squared, I end up with an answer of 9+ 4 root 5, which is wrong.

The correct answer is 20, which you get by doing the 2^2 which gives 4, and the (root5)^2 which gives 5, so you do 5*4=20 and that is the correct answer.

Why doesn't my method of expanding out the brackets work? When I expand it and multiply out, I get 4 + (2 root 5) + (2 root 5) +5 = 9 + (4 root 5).

Why doesnt that work??

Thanks!

Reply 1

Matte0

It's multiplication, not addition. If it was (2+rt5)^2, your answer would be right. In this case, you're multiplying, so (2rt5)^2 is the same as 4*5=20

(edited 7 years ago)

Reply 2

JustARandomer123

5

(2root5)(2root5) is the same as 2*2 multiplied by root5*root5 which is 4*5 which is 20

Reply 3

DarkEnergy

20

Original post by blobbybill

When I do it as (2 root 5)(2 root 5) because the bracket is squared, I end up with an answer of 9+ 4 root 5, which is wrong.

The correct answer is 20, which you get by doing the 2^2 which gives 4, and the (root5)^2 which gives 5, so you do 5*4=20 and that is the correct answer.

Why doesn't my method of expanding out the brackets work? When I expand it and multiply out, I get 4 + (2 root 5) + (2 root 5) +5 = 9 + (4 root 5).

Why doesnt that work??

Thanks!

Because it is (2root5) * (2root5), not (2 + root5) * (2 + root5).

Let's say root5 = x
The question is asking for (2x) * (2x)
But you're doing (2 + x) * (2 + x)

It's multiplication, so you don't use the ac+ad+bc+bd (or a^2 + 2ab + b^2) rule, you just expand to (2*2)*((5^.5)*(5^.5)) --> 20

Reply 5

JustARandomer123

5

Original post by blobbybill

When I do it as (2 root 5)(2 root 5) because the bracket is squared, I end up with an answer of 9+ 4 root 5, which is wrong.

The correct answer is 20, which you get by doing the 2^2 which gives 4, and the (root5)^2 which gives 5, so you do 5*4=20 and that is the correct answer.

Why doesn't my method of expanding out the brackets work? When I expand it and multiply out, I get 4 + (2 root 5) + (2 root 5) +5 = 9 + (4 root 5).

Why doesnt that work??

Thanks!

Sorry about the quality of the picture. Let me know if you need help

Reply 6

TheConfusedMedic

21

You're squaring (2 + root5) instead of (2 x root5).

(2 x root5)^2
= (2 x root5)(2 x root5)

because it's just all multiplication, you don't need the brackets:

2 x root5 x 2 x root5

multiplication can be done in any order so:

2 x 2 x root5 x root5
= 4 x 5
= 20

Reply 7

Plagioclase

21

Original post by blobbybill

When I do it as (2 root 5)(2 root 5) because the bracket is squared, I end up with an answer of 9+ 4 root 5, which is wrong.

The correct answer is 20, which you get by doing the 2^2 which gives 4, and the (root5)^2 which gives 5, so you do 5*4=20 and that is the correct answer.

Why doesn't my method of expanding out the brackets work? When I expand it and multiply out, I get 4 + (2 root 5) + (2 root 5) +5 = 9 + (4 root 5).

Why doesnt that work??

Thanks!

You've worked out the answer to

(2+\sqrt{5})^2

. The question is actually

(2\sqrt{5})^2 = 2^2\sqrt{5}^2 = 4\times5 = 20

.

Reply 8

username2902610

2

Original post by blobbybill

When I do it as (2 root 5)(2 root 5) because the bracket is squared, I end up with an answer of 9+ 4 root 5, which is wrong.

The correct answer is 20, which you get by doing the 2^2 which gives 4, and the (root5)^2 which gives 5, so you do 5*4=20 and that is the correct answer.

Why doesn't my method of expanding out the brackets work? When I expand it and multiply out, I get 4 + (2 root 5) + (2 root 5) +5 = 9 + (4 root 5).

Why doesnt that work??

Thanks!

The answer would be 20. Look at other user's working out.

Why doesn't this (2root5)^2 simplify properly when I expand the brackets?

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