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If a and b are integers and (3√a*√b)^6 = 500, then a + b cou

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Bunuel
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If a and b are integers and (3√a*√b)^6 = 500, then a + b cou [#permalink] New post   21 Nov 2017, 00:58
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If a and b are integers and \((\sqrt[3]{a}*\sqrt{b})^6 = 500\), then a + b could equal

A. 2
B. 3
C. 4
D. 5
E. 6


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B
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Re: If a and b are integers and (3√a*√b)^6 = 500, then a + b cou [#permalink] New post   01 Dec 2017, 21:40
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Bunuel wrote:
If a and b are integers and \((\sqrt[3]{a}*\sqrt{b})^6 = 500\), then a + b could equal

A. 2
B. 3
C. 4
D. 5
E. 6




From the above equation we get,

\([(a^{1/3}) X (b^{1/2})]^6 = 500\)

or\(a^2 X b^3 = 5^3 X 2^2\)

Thus we can write as , a= 2 and b = 5.

But a+b = 7 that is not in the option. However a could be = 2 or -2 (since square of any negative number is positive)

that is \(2^2 = (-2)^2\)

Now when a= -2 and b= 5, we have = -2 + 5 =3 . Hence option B
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If a and b are integers and [#permalink] New post   21 Nov 2018, 09:54
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If a and b are integers and \(( \sqrt[3]{a} * \sqrt{b} )^6 = 500\), the \(a + b\) could equal

A. 2

B. 3

C. 4

D. 5

E. 6
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Salsanousi
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Re: If a and b are integers and [#permalink] New post   23 Nov 2018, 13:29
Carcass wrote:
If a and b are integers and \(( \sqrt[3]{a} * \sqrt{b} )^6 = 500\), the \(a + b\) could equal

A. 2

B. 3

C. 4

D. 5

E. 6


(a^1/3 * b^1/2)^6 = a^2 * b^3 = 500

500 = 5 * 100 = 5 * 10 * 10 = 5 * 2 * 5 * 2 * 5 = 2^2 * 5*^3




2^2 * 5^3 = 4 * 125 = 500

a = -2 or 2

2 + 5 = 7 or -2 + 5 = 3

Answer choice B
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Re: If a and b are integers and [#permalink] New post   27 Nov 2018, 06:53
is it from the book?
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Re: If a and b are integers and [#permalink] New post   27 Nov 2018, 06:54
thanks alot
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If a and b are integers and [#permalink] New post   11 Dec 2018, 14:15
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If \(a\) and \(b\) are integers and \(( \sqrt[3]{a} * \sqrt{b} )^6 = 500\), then \(a + b\) could equal

A. 2

B. 3

C. 4

D. 5

E. 6
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HappyMathtutor
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Re: If a and b are integers and [#permalink] New post   17 Dec 2018, 20:47
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distribute the exponents, and you get

a^2*b^3 =500
start with a=2, then 2^2*b^3=500
4b^3=500
b^3=125
b=5
but a=b =2+5=7...no option for 7 there.
set a = (-2)
then -2+5=3

the answer is B
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chetan2u
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Re: If a and b are integers and [#permalink] New post   18 Dec 2018, 07:49
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Carcass wrote:
If \(a\) and \(b\) are integers and \(( \sqrt[3]{a} * \sqrt{b} )^6 = 500\), then \(a + b\) could equal

A. 2

B. 3

C. 4

D. 5

E. 6



\(( \sqrt[3]{a} * \sqrt{b} )^6 = 500.........a^{\frac{6}{3}}*b^{\frac{6}{2}}=2^25^3.......a^2b^3=2^25^3\)...
so b = 5, and a = 2 or -2..
we rae looking for a+b, so two possibilities - 5+2=7 and 5-2=3

3 is in choices so B
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Re: If a and b are integers and (3a*b)^6 = 500, then a + b cou [#permalink] New post   01 May 2023, 02:35
Hello from the GRE Prep Club BumpBot!

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