98^(1/2) + 72^(1/2) =

Question

\sqrt{98}+ \sqrt{72} =

A.  \sqrt{170}

B.  \sqrt{232}

C.  \sqrt{286}

D.  \sqrt{338}

E.  \sqrt{420}

rencsee · Accepted Answer

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broall · Answer

First make the prime factorization:

$98 = 2 \times 49 = 2 \times 7^2$
$72=2 \times 36 =2 \times 6^2 $

$\implies \sqrt{98}+\sqrt{72}=\sqrt{2 \times 7^2} + \sqrt{2 \times 6^2 } = 7\sqrt{2} + 6 \sqrt{2}=13\sqrt{2}=\sqrt{13^2 \times 2} = \sqrt{169 \times 2}=\sqrt{338}$

The answer is D

BrentGMATPrepNow · Answer

We can also solve this question with some  approximation 
Here are a few "nice" roots"
√49 = 7
√64 = 8
√81 = 9
√100 = 10

Since √98 is BETWEEN √81 and √100, we know that √98 is BETWEEN 9 and 10
Also, since √98 is VERY CLOSE to √100, we can conclude that √98 is much closer to 10 than it is to 9
So, we might say that √98 ≈ 9.8 or 9.9

Likewise, since √72 is BETWEEN √64 and √81, we know that √72 is BETWEEN 8 and 9
Here, √72 is pretty much halfway between √64 and √81, we might say that √72 ≈ 8.5

NOTE: As we'll soon see, we don't need to be super accurate with our approximations. 
We have: √98 + √72 ≈ 9.9 + 8.5 = ≈18.4

Now let's examine a few more "nice" roots"
17² = 289. So, √289 = 17
18² = 324. So, √324 = 18
19² = 361. So, √361 = 19
Since 18.4 is BETWEEN 18 and 19, we're looking for an answer choice that is BETWEEN √324 and √361
Since √338 is the ONLY answer choice BETWEEN √324 and √361, the correct answer must be D

Cheers,
Brent

guptarahul · Answer

98−−√+72−−√=98+72=

A. 170−−−√170

B. 232−−−√232

C. 286−−−√286

D. 338−−−√338

E. 420−−−√420

danlew · Answer

Prime factorization of 98 gives 2*(7^2)
Prime factorization of 72 gives (2^3)*(3^2)

From here we can take  \sqrt{2}  as a common factor and get D as the answer

GMATinsight · Answer

EASY WAY OUT FOR SUCH QUESTIONS IS  APPROXIMATION

\sqrt{98}+ \sqrt{72} =9.9+8.6 =   18.5

A.  \sqrt{170} = 13.1 approx.

B.  \sqrt{232}= 15.2 approx.

C.  \sqrt{286}= 16.5 approx.

D.  \sqrt{338}= 18.2 approx.     CORRECT ANSWER

E.  \sqrt{420}= 20.5 approx.

Nunuboy1994 · Answer

\sqrt{98} reduces to

49 x 2=
 7\sqrt{2} +...

\sqrt{72}
Reduces to 36 x 2
6\sqrt{2}

7\sqrt{2} + 6\sqrt{2} = 13 \sqrt{2}

169 x 2= 338

Abhishek009 · Answer

\sqrt{98}+ \sqrt{72}

Or,  7\sqrt{2}+ 6\sqrt{2}

Or,  13\sqrt{2}

\sqrt{338}  (When we take 13 inside the square root ), hence answer will be (D)

shashankism · Answer

\sqrt{98}+ \sqrt{72} 
 = 7\sqrt{2}+ 6\sqrt{2} 
 = 13\sqrt{2}

= \sqrt{338}

Answer D.

JeffTargetTestPrep · Answer

Let’s simplify the given expression:
 
√98 + √72 = √49 x √2 + √36 x √2 = 7√2 + 6√2 = 13√2
 
Since 13 = √169, 13√2 = √169 x √2 = √338.
 
Answer: D

arvind910619 · Answer

D
√98+√72=7√2+6√2=13√2=√169*2=√338

ehsan090 · Answer

For these questions I recommend two things
1. Learn Squares upto 30
2. Learn root equivalent
Now Solve
√98+√72
7√2+6√2
√2(7+6)
13√2 by approximation(√2=1.41)
13*1.4=18.2
18=324
19=361
So option D is correct choice

testcracker · Answer

easy way ( √98+ √72 ) ^2 =96 + 72 + 2*√(2*49*36*2) = √338 hope this helps

ScottTargetTestPrep · Answer

√98 + √72 = √49 x √2 + √36 x √2 = 7√2 + 6√2 = 13√2 = √169 x √2 = √338

Answer: D

EMPOWERgmatRichC · Answer

Hi All,

While this question might look a bit 'scary', the answer choices are 'spread out' enough that you can use them 'against' the prompt, do a bit of estimation and get the correct answer without too much trouble.

To start, 98 is fairly close to 100, so we can estimate the value of the first radical to be 10. 
In addition, 72 is clearly more than 64, so we know that the value of the second radical is a bit more than 8. 
Thus, we're looking for an answer that's fairly close to 18.

18^2= 324 and there's only one answer that's close to that....

Final Answer:  D

GMAT assassins aren't born, they're made, 
Rich

ThatDudeKnows · Answer

The answer choices are pretty spread out. Let's just Ballpark!

\sqrt{98}  is 10. Oh, it's not? Sure.

\sqrt{72}  is what, 8.5?

10+8.5 = 18.5

18^2  = 324. We need something just a little bigger than that.

Answer choice D.

ThatDudeKnowsBallparking

bumpbot · Answer

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98^(1/2) + 72^(1/2) =

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