sandy wrote:
Which of the following is closest to \(\sqrt{2.3 * 10^9}\)?
A. 50,000
B. 150,000
C. 500,000
D. 1,500,000
E. 5,000,000
Always scan the answer choices
BEFORE performing any calculations.
Since the answer choice are very spread apart, we can be very aggressive with our estimation.
We're going to use a nice rule that says
√(ab) = (√a)(√b)We have √(2.3 x 10⁹)
Since 2.3 isn't an easy number to find the square root of, the above
rule doesn't help us much.
However, what if we do the following:
√(2.3 x 10⁹) = √(2.3 x 10¹ x 10⁸)
= √(23 x 10⁸)
How does this help?
Well, 23 is pretty close to 25 and we know that √25 = 5.
Can we do this? You bet. Remember that since the answer choice are very spread apart, we can be very aggressive with our estimation
We get:
√(23 x 10⁸) = (√23)(√10⁸)
≈ 5(10⁴)
≈ 5(10,000)
≈ 50,000
Answer: A
Cheers,
Brent
_________________
Brent Hanneson – Creator of greenlighttestprep.com
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50% (01:33) correct
