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# (245^(1/2) - 75^(1/2))^2 =

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Math Expert
Joined: 02 Sep 2009
Posts: 58445
(245^(1/2) - 75^(1/2))^2 =  [#permalink]

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28 Oct 2018, 23:31
00:00

Difficulty:

15% (low)

Question Stats:

87% (01:30) correct 13% (02:01) wrong based on 38 sessions

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$$(\sqrt{245}-\sqrt{75})^2=$$

A. $$170 -5\sqrt{8}$$

B. $$170 -70\sqrt{15}$$

C. $$320 -70\sqrt{15}$$

D. $$318 -35\sqrt{15}$$

E. $$170$$

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(245^(1/2) - 75^(1/2))^2 =  [#permalink]

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Updated on: 29 Oct 2018, 00:11
$$(a-b)^2 = a^2+b^2-2ab$$

$$(\sqrt{245}-\sqrt{75})^2$$
= $$245+75-2\sqrt{245}\sqrt{75}$$
= $$320-2*7\sqrt{5}*5\sqrt{3}$$
= $$320-70\sqrt{15}$$

C is the answer.
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Originally posted by Chethan92 on 28 Oct 2018, 23:45.
Last edited by Chethan92 on 29 Oct 2018, 00:11, edited 1 time in total.
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Re: (245^(1/2) - 75^(1/2))^2 =  [#permalink]

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29 Oct 2018, 00:08
$$(a - b)^2 = a^2 + b^2 - 2ab$$

$$(\sqrt{245} - \sqrt{75})^2$$ = $$245 + 75 - 2 (7\sqrt{5}) (5\sqrt{3})$$

= $$320 - 70\sqrt{15}$$

OPTION : C
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Re: (245^(1/2) - 75^(1/2))^2 =   [#permalink] 29 Oct 2018, 00:08
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# (245^(1/2) - 75^(1/2))^2 =

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