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# If a, b and c have the values shown, which of the following shows

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Director
Joined: 12 Feb 2015
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If a, b and c have the values shown, which of the following shows  [#permalink]

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01 Dec 2019, 06:04
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a = $$\sqrt{2} + \sqrt{6}$$
b= $$\sqrt{3} + \sqrt{5}$$
c= 4

If a, b and c have the values shown, which of the following shows their order from least to greatest?

A) a, b, c

B) b, c, a

C) b, a, c

D) c, a, b

E) c, b, a

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Manish

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Re: If a, b and c have the values shown, which of the following shows  [#permalink]

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01 Dec 2019, 10:06
Let us take the square of a , b , and c and compare the squares
$$a^2 = (\sqrt{2} + \sqrt{6})^2)= 2+6+2*(\sqrt{12})$$
$$b^2 = (\sqrt{3} + \sqrt{5})^2) = 3+5+2*(\sqrt{15})$$
$$c^2$$ = 16

Now it is clear that $$8+2*(\sqrt{12})<8+2*(\sqrt{15})<16$$
Hence $$a^2<b^2<c^2$$
or, $$a<b<c$$

CAMANISHPARMAR wrote:
a = $$\sqrt{2} + \sqrt{6}$$
b= $$\sqrt{3} + \sqrt{5}$$
c= 4

If a, b and c have the values shown, which of the following shows their order from least to greatest?

A) a, b, c

B) b, c, a

C) b, a, c

D) c, a, b

E) c, b, a

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VP
Joined: 19 Oct 2018
Posts: 1151
Location: India
Re: If a, b and c have the values shown, which of the following shows  [#permalink]

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01 Dec 2019, 10:22
a=$$\sqrt{2} + \sqrt{6}$$

$$a^2$$= $$2+6+2\sqrt{6*2}$$= $$8+2\sqrt{12}$$

b= $$\sqrt{3} + \sqrt{5}$$

$$b^2$$= $$3+5+2\sqrt{5*3}$$= $$8+2\sqrt{15}$$

c= 2+2= $$\sqrt{4} + \sqrt{4}$$

$$c^2$$= $$4+4+2\sqrt{4*4}$$= $$8+2\sqrt{16}$$

$$\sqrt{12}<\sqrt{15}<\sqrt{16}$$

a<b<c

CAMANISHPARMAR wrote:
a = $$\sqrt{2} + \sqrt{6}$$
b= $$\sqrt{3} + \sqrt{5}$$
c= 4

If a, b and c have the values shown, which of the following shows their order from least to greatest?

A) a, b, c

B) b, c, a

C) b, a, c

D) c, a, b

E) c, b, a
Re: If a, b and c have the values shown, which of the following shows   [#permalink] 01 Dec 2019, 10:22
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