Root(80)+root(125)

Question

\sqrt{80}+\sqrt{125} =

(A)  9\sqrt{5} 
(B)  20\sqrt{5} 
(C)  41\sqrt{5} 
(D)  \sqrt{205} 
(E) 100

Bunuel · Accepted Answer

SOLUTION

\sqrt{80}+\sqrt{125} =

(A)  9\sqrt{5} 
(B)  20\sqrt{5} 
(C)  41\sqrt{5} 
(D)  \sqrt{205} 
(E) 100

\sqrt{80}+\sqrt{125} =\sqrt{16*5}+\sqrt{25*5}=4\sqrt{5}+5\sqrt{5}=9\sqrt{5} .

Answer: A.

Carcass · Answer

Whe we deal with this problems may be the best thing to do is to break the number into factors

\sqrt{80}  =  \sqrt{2*5*2*2*2}  --->  \sqrt{4*4*5}  --->  4  \sqrt{5}

\sqrt{125}   =   \sqrt{25 *5}  ----->  5   \sqrt{5}

4  \sqrt{5}   + 5   \sqrt{5}   =   9  \sqrt{5}

A should be the answer

Muki · Answer

\sqrt{80} = \sqrt{16*5} = 4\sqrt{5}  ........(1)

\sqrt{125} = \sqrt{25*5} = 5\sqrt{5}  .......(2)

Thus  4\sqrt{5} + 5\sqrt{5} = 9\sqrt{5}

Thus answer is A

aeglorre · Answer

The only thing I know is that the answer is just under 24.. And it is definitely not D since D falls between 14 and 15.. And it's clearly not E. And out of the 3 left, B and C are waay too high above 24, and I figured sqrrt of 5 is around "2.something" so A made most sense.

Clearly this approach is very shaky but this time it worked.

Dienekes · Answer

\sqrt{80}  is approx. 9 and  \sqrt{125}  is approx. 11 so the answer should be close to 20. Choice A is the closest.

erikvm · Answer

I see this question is from a subcategory called "Practice Questions", where can I find that sub?

Bunuel · Answer

Those are practice questions from OG13. You can find all questions  HERE .

ScottTargetTestPrep · Answer

Solution:

To solve the problem we must simplify the radicals. Radicals should be simplified whenever possible. Since the square root of a perfect square produces integers, it will often be helpful to locate and simplify perfect squares within a radical expression. Thus, we first locate the perfect squares that divide evenly into 80 and 125, making the simplification of each radical straightforward.

√80 = √16 x √5 = 4√5

√125 = √25 x √5 = 5√5

Now we can add these two results together. Remember to keep the value inside the radical constant and add together the values on the outside.

4√5 + 5√5 = 9√5

The answer is A.

aishkar · Answer

A
80=4*4*5
125=5*5*5
Root(80)=4Root(5)
Similarly 125
hence 9Root(5)

Abhishek009 · Answer

\sqrt{80}+\sqrt{125} =   4\sqrt{5}+5\sqrt{5}  =  9\sqrt{5}

Answer will be (A)

diegocml · Answer

Prime factorization can really help you and so can converting the roots to fraction exponents.

\sqrt { 80 } +\sqrt { 125 } =\ { ({ 2 }^{ 4 } }	imes { 5 }^{ 1 })^{ \frac { 1 }{ 2 } }+{ ({ 5 }^{ 2 }	imes { 5 }^{ 1 }) }^{ \frac { 1 }{ 2 } }=\ ({ 2 }^{ \frac { 4 }{ 2 } }	imes { 5 }^{ \frac { 1 }{ 2 } })+({ 5 }^{ \frac { 2 }{ 2 } }	imes { 5 }^{ \frac { 1 }{ 2 } })\quad =\ { 2 }^{ 2 }\sqrt { 5 } +5\sqrt { 5 } =\ 4\sqrt { 5 } +5\sqrt { 5 } =\ \Rightarrow 9\sqrt { 5 } \

nkmungila · Answer

√80 ~~ 9
√ 125 ~~ 11
9+11 = 20
√5 ~~2.1
9*2.1~~20
all other answer not near to this
Hence answer must be A

gmat1393 · Answer

\sqrt{80}  =  \sqrt{16*5}  --->  \sqrt{4*4*5}

\sqrt{125}   =   \sqrt{25 *5}  ----->  5   \sqrt{5}

= 9  \sqrt{5}

D4kshGargas · Answer

Try  approximation

√80 ≈ √81 i.e. < 9
√125 ≈ √121 i.e. 11 < value < 12

Therefore sum would be 11.something + (8.9+ something but less than 9)
i.e. ≈ 19

and we know √5 is ≈ 2 as √4 = 2

And 9 * 2 = 18

So (A) is the nearest answer.

GMATinsight · Answer

\sqrt{80} + \sqrt{125} ≈ 9+11 ≈ 20

A.  9\sqrt{5} ≈9*2.4≈21  CORRECT 
B.  20\sqrt{5}  IMPOSSIBLE 
C.  41\sqrt{5}  IMPOSSIBLE 
D.  \sqrt{205} ≈14  IMPOSSIBLE 
E. 100  IMPOSSIBLE

AnirudhaS · Answer

√80+√125
=4√5+5√5
=9√5

Answer:  A

Aboyhasnoname · Answer

Lets do like this....

m]\sqrt{80}+\sqrt{125} =

So \sqrt{80} should be around 9 Since...9^2 = 81... 
and \sqrt{125} Should be around 11.xx since 11^2 is 125... 
Add them..answer should be near 20.....B,C,E are way above 20 ......
D. \sqrt{205} is way to less ....as 15^2 only is 225...

ablatt4 · Answer

simplify under the root

Sqrt 80= Sqrt 4*4*5 = 2*2 sqrt 5

Sqrt 125 = Sqrt 5*5*5 = 5 sqrt 5

2*2+5 = 9

ablatt4 · Answer

80=2^4*5
125+5^3

sqrt 80=4 sqrt 5
sqrt 125= 5 sqrt 5

Root(80)+root(125)

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Root(80)+root(125)

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