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Re: (4.8*10^9)^(1/2) is closest in value to [#permalink]

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18 Oct 2015, 13:36

rewrite everything as

(48*10^8)^1/2 we get 48^1/2 * 10^4 48^1/2 is 4*sqrt(3) which is ~6.8 6.8 * 10^4 = aprox 68k the only closest answer we have is 70k, which should be the correct answer choice.

Re: (4.8*10^9)^(1/2) is closest in value to [#permalink]

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02 May 2016, 15:59

Using some critical thinking here, we know that √4.8*10^9 = √48*10^8 = (√48) * 10^4

(√48) * 10^4 is (√16*3)*10^4 4√3 is a little less than 4*2, so you know from looking at the answers it's either B or D Since it's 10^4, just count zeros, and you have B

We are given √(4.8 x 10^9), and we need to determine the answer choice that is closest in value. We first simplify the expression by eliminating the decimal point in 4.8. To do this, we can move the decimal one place to the right to get 48 and simultaneously reduce 10^9 to 10^8. So we need to estimate √(48 x 10^8). Notice that 48 is very close to 49, which is a perfect square. Note, too, that the square root of 10^8 is easy to calculate because the exponent is now an even number. So let’s evaluate √(49 x 10^8):

√(49 x 10^8)

√(49) x √(10^8)

7 x 10^4

70,000

Thus √(4.8 x 10^9) ≈ 70,000.

Answer: B
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