I bet there's an easier way to solve this but this is how I did it:
[sqrt(9+sqrt80)+sqrt(9-sqrt80)] * [sqrt(9+sqrt80)+sqrt(9-sqrt80)]
=9+sqrt(80)+2sqrt(9+sqrt80)*sqrt(9-sqrt80)+9-sqrt80
sqrt 80's cancel and you're left with:
18+2sqrt(9+sqrt80)*sqrt(9-sqrt80)
Since you're multiplying two radicals, you can multiply the inside terms and make it into one radical.
18+2sqrt(81-80)=18+2=20 E
quadratics
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truplayer256
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Mustang
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I found a slightly easier way
the original question is in the form: (a+b)^2 where a= sqrt (9+sqrt(80))
and b is : sqrt (9-sqrt(80))
(a+b)^2= a^2 + b^2 + 2*a*b
Substituting the above values we get
9+ sqrt(80)+9 - sqrt(80) + 2 *[sqrt(9+ sqrt(80)) *sqrt(9-sqrt(80))]
= 18 + 2*[sqrt{ (9+ sqrt(80)) *(9-sqrt(80))} ]
the expression within [] is of form (a+b)(a-b) = a^2 -b^2
a=9
b= sqrt(80)
solve it to get answer 20
the original question is in the form: (a+b)^2 where a= sqrt (9+sqrt(80))
and b is : sqrt (9-sqrt(80))
(a+b)^2= a^2 + b^2 + 2*a*b
Substituting the above values we get
9+ sqrt(80)+9 - sqrt(80) + 2 *[sqrt(9+ sqrt(80)) *sqrt(9-sqrt(80))]
= 18 + 2*[sqrt{ (9+ sqrt(80)) *(9-sqrt(80))} ]
the expression within [] is of form (a+b)(a-b) = a^2 -b^2
a=9
b= sqrt(80)
solve it to get answer 20
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sureshbala
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Folks, this can be answered quite easily without getting into too much of calculation.
Look at this....
Look at this....
How do you multiply sqrt (a+b) by sqrt (a+b)?
Also, how do you multiply sqrt (a+b) by sqrt (a-b)?
I like the above explanation but am having a difficult time multiplying square roots when there is more than one term under the sign. Thanks in advance!
Also, how do you multiply sqrt (a+b) by sqrt (a-b)?
I like the above explanation but am having a difficult time multiplying square roots when there is more than one term under the sign. Thanks in advance!
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BuckeyeT
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mdavis,
To your first question -
For like termed exponents, add the terms when multiplying. For example, (2^n)(2^m)=2^(n+m)
Specifically, sqrt (a+b) can be rewritten as (a+b)^(1/2). So, sqrt (a+b) * sqrt (a+b) = [(a+b)^(1/2)] * [(a+b)^(1/2)] = (a+b)^((1/2)+(1/2)) = (a+b)^1 = a+b.
To your second question -
As truplayer256 mentioned,
Does that help explain it a bit better?
To your first question -
For like termed exponents, add the terms when multiplying. For example, (2^n)(2^m)=2^(n+m)
Specifically, sqrt (a+b) can be rewritten as (a+b)^(1/2). So, sqrt (a+b) * sqrt (a+b) = [(a+b)^(1/2)] * [(a+b)^(1/2)] = (a+b)^((1/2)+(1/2)) = (a+b)^1 = a+b.
To your second question -
As truplayer256 mentioned,
So, multiply out the terms and slap them inside the radical (sqrt). sqrt (a+b)*sqrt (a-b) = sqrt (a^2-ab+ab+b^2) = sqrt (a^2+b^2).Since you're multiplying two radicals, you can multiply the inside terms and make it into one radical.
Does that help explain it a bit better?
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sureshbala
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Dear friend,mdavis wrote:How do you multiply sqrt (a+b) by sqrt (a+b)?
Also, how do you multiply sqrt (a+b) by sqrt (a-b)?
I like the above explanation but am having a difficult time multiplying square roots when there is more than one term under the sign. Thanks in advance!
We have the following simple rule regarding square roots.
sqrt(p) x sqrt(q) = sqrt(pq)
So sqrt(a+b) x sqrt(a-b) = sqrt[(a+b)(a-b)] = sqrt[a^2 - b^2]. I applied the same rule in my explanation
