Expand: sqrt2(3+sqrt3)
Answer is 3sqrt2 + sqrt6
My question is, why don't we distribute the sqrt 2 across both terms --> 3sqrt2 + sqrt 6. Then break sqrt 6 into (sqrt 2)(sqrt 3). From here we would take 1sqrt 2 and add it to our 3sqrt2 to get 4sqrt2+sqrt3.
Am I missing something?
Simple Root Problem
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- theCodeToGMAT
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- theCodeToGMAT
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Steven your doubt is something like: 2*3 = 6 = 2*3
At first you are combining them and then you are splitting them.
3sqrt2 + sqrt 6 --> here if you again take break sqrt(6) into sqrt(2) & sqrt(3).. and then take common.. then would will again reach to starting point; that is, you are reversing the steps you performed
(sqrt2)[3+(sqrt3)]
= 3*sqrt(2) + sqrt(2)*sqrt(3)
= 3*sqrt(2) + sqrt(6)
= 3*sqrt(2) + sqrt(2)*sqrt(3)
(sqrt2)[3+(sqrt3)]
At first you are combining them and then you are splitting them.
3sqrt2 + sqrt 6 --> here if you again take break sqrt(6) into sqrt(2) & sqrt(3).. and then take common.. then would will again reach to starting point; that is, you are reversing the steps you performed
(sqrt2)[3+(sqrt3)]
= 3*sqrt(2) + sqrt(2)*sqrt(3)
= 3*sqrt(2) + sqrt(6)
= 3*sqrt(2) + sqrt(2)*sqrt(3)
(sqrt2)[3+(sqrt3)]
R A H U L
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Hi stevennu,
The "short answer" to your question is that (sqrt2)(sqrt3) = sqrt6...... so yes, it's one term and can't be mathematically "split" the way you're describing.
It's similar to this:
X + X^2 = X + (X)(X)
But you can't "split off" an X and add it to the first X.
X + (X)(X) CANNOT be rewritten as 2X + X
GMAT assassins aren't born, they're made,
Rich
The "short answer" to your question is that (sqrt2)(sqrt3) = sqrt6...... so yes, it's one term and can't be mathematically "split" the way you're describing.
It's similar to this:
X + X^2 = X + (X)(X)
But you can't "split off" an X and add it to the first X.
X + (X)(X) CANNOT be rewritten as 2X + X
GMAT assassins aren't born, they're made,
Rich
- sanju09
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I hope it's (3 + √3) √2, then 3√2 + √2√3 is the next step. Now, how on earth can we snatch that √2 from √3 to nurture 3√2?stevennu wrote:Expand: sqrt2(3+sqrt3)
Answer is 3sqrt2 + sqrt6
My question is, why don't we distribute the sqrt 2 across both terms --> 3sqrt2 + sqrt 6. Then break sqrt 6 into (sqrt 2)(sqrt 3). From here we would take 1sqrt 2 and add it to our 3sqrt2 to get 4sqrt2+sqrt3.
Am I missing something?
You are missing this point...
We can pick and add only what's free for it. Our √2 is already engaged with √3, and the name of that nuptial knot is "multiplied together", means "it's not free for it".
3√2 + √6 is the correct answer in its correct form.
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
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Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
- sanju09
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Vodka or Country Made?stevennu wrote:Thanks all! I really appreciate the thorough responses. I'd buy you all a drink if I could.
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com