35\(\sqrt{2}\)= \(\sqrt{35*35*2}\)= \(\sqrt{2450}\)

Answer: E.
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Kindly hit kudos if my post helps!

Here's another approach...

2450 is a little bit less than 2500

So, √2450 will be a little bit less than √2500

√2500 = 50, so the correct answer will be a little bit less than 50

IMPORTANT: Before test day, you should memorize the following approximations:
√2 ≈ 1.4
√3 ≈ 1.7
√5 ≈ 2.2

Now let's use this info to check the answer choices
A. 25√2 ≈ (25)(1.4) ≈ 35 ELIMINATE

B. 35 ELIMINATE

C. 28√2 ≈ (28)(1.4) ≈ 40 ELIMINATE

D. 49 This answer choice is close to 50. HOWEVER, we can see that 49² will have units digit 1, while 2450 has units digit 0. ELIMINATE

E. 35√2
By the process of elimination, the correct answer must be E
If we want to confirm, we can recognize the following:
35√2 = (√35²)(√2)
= (√1225)(√2)
= √2450
BINGO!!
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Brent Hanneson – GMATPrepNow.com

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We see that 2450 ends with 50 which means it’s divisible by 5^2 = 25. Since 2450/25 = 98 and 98 = 49 x 2, we have 2450 = 25 x 49 x 2. Thus

√2450 = √(25 x 49 x 2) = √25 x √49 x √2 = 5 x 7 x √2 = 35√2

Answer: E
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