Radical Expressions: 2 sqrt 75/16 + 4 sqrt 8/sqrt32

John Whitaker

Junior Member
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May 9, 2006
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The problem and book solution is:

2 sqrt 75/16 + 4 sqrt 8/sqrt32
= 2 sqrt 25*3/sqrt 16 + 4 sqrt 4*2/sqrt 16*2
= 2(5 sqrt 3/4) + 4(2 sqrt 2/4 sqrt 2)
= 5 sqrt 3/2 + 2
= 5 sqrt 3/2 + 4/2
… and I don’t know where that 4 (in 4/2) comes from.
= 5 sqrt 3 + 4 /2 (final answer)

Thank you.
John Whitaker
 
Re: Radical Expressions

John Whitaker said:
The problem and book solution is:

2 sqrt 75/16 + 4 sqrt 8/sqrt32
= 2 sqrt 25*3/sqrt 16 + 4 sqrt 4*2/sqrt 16*2
= 2(5 sqrt 3/4) + 4(2 sqrt 2/4 sqrt 2)
= 5 sqrt 3/2 + 2
= 5 sqrt 3/2 + 4/2
… and I don’t know where that 4 (in 4/2) comes from.<<< It was 2/1 before - multiplied top and bottom by 2
= (5 sqrt 3 + 4)/2 (final answer)

Thank you.
John Whitaker

\(\displaystyle 2\sqrt\frac{75}{16} \, + \, 4\frac{\sqrt 8}{\sqrt {32}}\)

\(\displaystyle =\, 2\cdot\frac{5\sqrt 3}{4} \, + \, 4\cdot \frac{2\sqrt 2}{4\sqrt {2}}\)
 
I'm sorry... still don't get it. Can you show me where I am to do this?
Thank you.
John Whitaker :wink:
 
Re: Radical Expressions

I'll give it a try... Basically we're trying to get a common denominator so we can add the numerators and put the whole thing over one denominator. This could come in handy, and a fraction plus a fraction is usually harder to work with than just a fraction. :)

\(\displaystyle 2\sqrt\frac{75}{16} \, + \, 4\frac{\sqrt 8}{\sqrt {32}}\)

\(\displaystyle =\, 2\cdot\frac{5\sqrt 3}{4} \, + \, 4\cdot \frac{2\sqrt 2}{4\sqrt {2}}\)

That's where we got above. We can take 2/4 = 1/2 for the first term and 4/4 = 1 AND sqrt(2)/sqrt(2) = 1 for the second term. Now,

\(\displaystyle =\, \frac{5 \sqrt 3}{2} \, + \, 2\)

Multiply the second term by the equivalent of 1, or by \(\displaystyle \frac{2}{2}\). That gives you the common denominator of 2 for both terms.
 
John Whitaker said:
2 sqrt 75/16 2 sqrt(75)/16 OR 2 sqrt(75/16)

2 sqrt 25*3/sqrt 16 2 sqrt(25) * 3/sqrt(16) OR 2 sqrt(25*3)/sqrt(16)

2 sqrt 2/4 sqrt 2 2 sqrt(2)/4 * sqrt(2) OR 2 sqrt(2/4) * sqrt(2) OR [2 sqrt(2)]/[4 sqrt(2)]


Hi John:

As you can see, typing math expressions can lead to ambiguity if not properly done. (In this particular thread, your work plus context allowed people to figure out what you meant. Other times, we may not be able to figure it out.)

In the future, please use grouping symbols like () and [] and {} to show clearly what is under the square root symbol and what denominators and numerators are in fractions involving more than one symbol over another.

EG:

sqrt(radicand goes here)

[expression for numerator]/[expression for denominator]

Cheers,

~ Mark :)

 
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