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is closest in value to

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by Vincen » Mon Oct 23, 2017 7:01 pm
$$\sqrt{4.8\cdot10^9}$$ is closest in value to

(A) 2,200
(B) 70,000
(C) 220,000
(D) 7,000,000
(E) 22,000,000

The OA is B.

How can I compute this value? Experts, I ask for your help.
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by Jay@ManhattanReview » Tue Oct 24, 2017 1:09 am
Vincen wrote:$$\sqrt{4.8\cdot10^9}$$ is closest in value to

(A) 2,200
(B) 70,000
(C) 220,000
(D) 7,000,000
(E) 22,000,000

The OA is B.

How can I compute this value? Experts, I ask for your help.
$$\sqrt{4.8\cdot10^9} = \sqrt{48\cdot10^8} = ~7\sqrt{10^8} = 7\cdot10^4 = 70,000$$

The correct answer: B

Hope this helps!

-Jay

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is closest in value to

by EconomistGMATTutor » Tue Oct 24, 2017 2:38 pm
$$\sqrt{4.8\cdot10^9}$$ is closest in value to

(A) 2,200
(B) 70,000
(C) 220,000
(D) 7,000,000
(E) 22,000,000

The OA is B.

How can I compute this value? Experts, I ask for your help.
Hi Vincen,
Let's take a look at your question.

We are asked to find the the closest value of $$\sqrt{4.8\cdot10^9}$$.
Let's write 10^9 as 10 x 10^8.


$$\sqrt{4.8\times10\times10^8}$$
$$=\sqrt{48\times10^8}$$
$$\approx\sqrt{49\times10^8}$$
$$\approx7\times10^4$$
$$\approx70,000$$

Therefore, Option B is correct.

Hope this helps.
I am available if you'd like any follow up.
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by Vincen » Thu Nov 02, 2017 8:59 am
Thank you EconomistGMATTutor.

It helped me a lot when you used the approximate symbol.
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by Brent@GMATPrepNow » Thu Nov 02, 2017 9:38 am
ASIDE: the above solutions take advantage of a very useful rule that says...
√(xy) = (√x) (√y)

This will save you time finding the square roots of big products.
For example, to evaluate √(81 x 64), we COULD find the product of 81 and 64 to get 5184
But this means we have to find √5184, which is awful!!

However, if we apply the above rule, we get: √(81 x 64) = (√81)(√64) = (9)(8) = 72

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Scott@TargetTestPrep » Fri Nov 01, 2019 6:54 pm
Vincen wrote:$$\sqrt{4.8\cdot10^9}$$ is closest in value to

(A) 2,200
(B) 70,000
(C) 220,000
(D) 7,000,000
(E) 22,000,000

The OA is B.

How can I compute this value? Experts, I ask for your help.
We can rewrite the expression as:

√(48 x 10^8)

which is approximately:

√49 x √10^8

7 x 10^4 = 70,000

Answer: B

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