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Math Expert V
Joined: 02 Sep 2009
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98^(1/2) + 72^(1/2) =  [#permalink]

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2
7 00:00

Difficulty:   25% (medium)

Question Stats: 76% (01:29) correct 24% (01:44) wrong based on 513 sessions

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

A. $$\sqrt{170}$$

B. $$\sqrt{232}$$

C. $$\sqrt{286}$$

D. $$\sqrt{338}$$

E. $$\sqrt{420}$$

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Re: 98^(1/2) + 72^(1/2) =  [#permalink]

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Re: 98^(1/2) + 72^(1/2) =  [#permalink]

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Bunuel wrote:
$$\sqrt{98}+ \sqrt{72} =$$

A. $$\sqrt{170}$$

B. $$\sqrt{232}$$

C. $$\sqrt{286}$$

D. $$\sqrt{338}$$

E. $$\sqrt{420}$$

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
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Re: 98^(1/2) + 72^(1/2) =  [#permalink]

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98−−√+72−−√=98+72=

A. 170−−−√170

B. 232−−−√232

C. 286−−−√286

D. 338−−−√338

E. 420−−−√420
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GMAT 1: 720 Q48 V40 Re: 98^(1/2) + 72^(1/2) =  [#permalink]

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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
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98^(1/2) + 72^(1/2) =  [#permalink]

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Bunuel wrote:
$$\sqrt{98}+ \sqrt{72} =$$

A. $$\sqrt{170}$$

B. $$\sqrt{232}$$

C. $$\sqrt{286}$$

D. $$\sqrt{338}$$

E. $$\sqrt{420}$$

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. $$\sqrt{420}= 20.5 approx.$$
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Re: 98^(1/2) + 72^(1/2) =  [#permalink]

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Bunuel wrote:
$$\sqrt{98}+ \sqrt{72} =$$

A. $$\sqrt{170}$$

B. $$\sqrt{232}$$

C. $$\sqrt{286}$$

D. $$\sqrt{338}$$

E. $$\sqrt{420}$$

\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
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Re: 98^(1/2) + 72^(1/2) =  [#permalink]

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Bunuel wrote:
$$\sqrt{98}+ \sqrt{72} =$$

A. $$\sqrt{170}$$

B. $$\sqrt{232}$$

C. $$\sqrt{286}$$

D. $$\sqrt{338}$$

E. $$\sqrt{420}$$

$$\sqrt{98}+ \sqrt{72}$$

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)
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Re: 98^(1/2) + 72^(1/2) =  [#permalink]

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Bunuel wrote:
$$\sqrt{98}+ \sqrt{72} =$$

A. $$\sqrt{170}$$

B. $$\sqrt{232}$$

C. $$\sqrt{286}$$

D. $$\sqrt{338}$$

E. $$\sqrt{420}$$

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

$$= \sqrt{338}$$

Answer D.

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Re: 98^(1/2) + 72^(1/2) =  [#permalink]

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Bunuel wrote:
$$\sqrt{98}+ \sqrt{72} =$$

A. $$\sqrt{170}$$

B. $$\sqrt{232}$$

C. $$\sqrt{286}$$

D. $$\sqrt{338}$$

E. $$\sqrt{420}$$

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
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Re: 98^(1/2) + 72^(1/2) =  [#permalink]

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D
√98+√72=7√2+6√2=13√2=√169*2=√338
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Re: 98^(1/2) + 72^(1/2) =  [#permalink]

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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
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98^(1/2) + 72^(1/2) =  [#permalink]

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Bunuel wrote:
$$\sqrt{98}+ \sqrt{72} =$$

A. $$\sqrt{170}$$

B. $$\sqrt{232}$$

C. $$\sqrt{286}$$

D. $$\sqrt{338}$$

E. $$\sqrt{420}$$

easy way

( √98+ √72 ) ^2

=96 + 72 + 2*√(2*49*36*2)

= √338

hope this helps Target Test Prep Representative D
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Re: 98^(1/2) + 72^(1/2) =  [#permalink]

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Bunuel wrote:
$$\sqrt{98}+ \sqrt{72} =$$

A. $$\sqrt{170}$$

B. $$\sqrt{232}$$

C. $$\sqrt{286}$$

D. $$\sqrt{338}$$

E. $$\sqrt{420}$$

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

Answer: D
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Re: 98^(1/2) + 72^(1/2) =  [#permalink]

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1
Top Contributor
Bunuel wrote:
$$\sqrt{98}+ \sqrt{72} =$$

A. $$\sqrt{170}$$

B. $$\sqrt{232}$$

C. $$\sqrt{286}$$

D. $$\sqrt{338}$$

E. $$\sqrt{420}$$

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
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: 98^(1/2) + 72^(1/2) =  [#permalink]

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1
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:

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Re: 98^(1/2) + 72^(1/2) =  [#permalink]

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