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# What is 157609^(1/2)?

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157609 is odd so its sq rt cannot be even. Eliminate B,C

Option E is 403, 400 is sq rt of 160000 which is greater than 157609. We are left with 323 and 397. Now 350 square is 122500 so 323 can be eliminated. Hence answer is d 397

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Since the units digit has to be 9 so only 323 and 397 will remain, then we can take a square of 320 and determine that 323 will not be our answer coz 320^2= 102400 so therefore D is our answer
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hazelnut wrote:
What is $$\sqrt{157609}$$?

(A) 323
(B) 378
(C) 392
(D) 397
(E) 403

$$400^2 = 160000$$
Also, for the last digit 9, the square root could be 3 or 7 because $$\sqrt{49} = 7$$ and $$\sqrt{9} = 3$$
Since the number in question is slightly below 160000, the square root cannot be 403.

Therefore, the number must be 397(Option D)

Another method to tests our answer is as follows:
$$(397)^2 = (400 - 3)^2 = 160000 + 9 - 2(400)(3) = 160009 - 2400 = 157609$$
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hazelnut wrote:
What is $$\sqrt{157609}$$?

(A) 323
(B) 378
(C) 392
(D) 397
(E) 403

We need a number whose square is 157609.

Answer choice B and C end with even number, therefore these two numbers can't give a number that ends with 9. Eliminate

Choice E is easier. We know 400 * 400 = 160000 (approx), more than our number. Eliminate

A and D, Solve for one on the two numbers and you will get the answer.

(D)
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hazelnut wrote:
What is $$\sqrt{157609}$$?

(A) 323
(B) 378
(C) 392
(D) 397
(E) 403

Since we are finding a number that when multiplied by itself will have a units digit of 9, we see that the units digit of that number must either be 3 or 7.

Thus, our only possible answers are A, D, and E.

Since 400 x 400 = 160,000, we see that E is too large..

Since 300 x 300 = 90,000 and 157,609 is much closer to 160,000 than it is to 90,000, we see that its square root should be closer to 400 than to 300, so thus the answer must be 397.

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Easy but have to get answer in less time!!!!
TRICK SAVEs TIME

400^2=16000
350^2=122500
Clearly, 157609 must be in b/w 350^2 to 400^2 i.e Option A & E is eliminated
Now since last digit of 157609 is 9 , We need to find a option whose last digit end up to 9 when squared.
Answer is one among [378 , 392 & 397]
378 => last digit 8 => 8^2=64 => last digit comes 4
392 => last digit 2 => 2^2=4 => last digit comes 4
397 => last digit 7 => 7^2=49 => last digit comes 9 = Match with last digit of 157609