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

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

Are You Up For the Challenge: 700 Level Questions

Even if we cannot recall the value of $$\sqrt{2}$$ or $$\sqrt{3}$$ or $$\sqrt{5}$$

As long as we keep $$\sqrt{6} > \sqrt{5} > \sqrt{3} > \sqrt{2}$$ we can take approximate values keeping in mind $$\sqrt{4} = 2$$ , $$\sqrt{9} =3$$ as reference points.

$$\sqrt{2} = 1.2$$( Purposefully taking a value different from the actual value ) I know it has to be more than $$1$$ but less than $$2$$

$$\sqrt{3} = 1.5$$ ( Purposefully taking a value different from the actual value ) I know it has be more than what value we have taken for $$\sqrt{2} = 1.2$$ but less than $$2$$

$$\sqrt{5} = 2.3$$ ( Purposefully taking a value different from the actual value ) I know it has to be more than $$2$$ but less than $$3$$

$$\sqrt{6}$$ = a value more than $$\sqrt{5}$$ but less than $$3$$ hence let us take it as $$2.5$$

$$a = \sqrt{2} + \sqrt{6} = 1.2 + 2.5 = 3.7$$

$$b= \sqrt{3} + \sqrt{5} = 1.5 +2.3 = 3.8$$

$$c = 4$$

$$a < b < c$$

Ans A

Hope it's clear.
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Re: If a, b and c have the values shown, which of the following shows thei [#permalink]
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Bunuel 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

The three numbers (a, b, and c) are positive, so their ascending order must follow the ascending order of their squares.

a^2 = 2 + 2√12 + 6 = 8 + √48

b^2 = 3 + 2√15 + 5 = 8 + √60

c^2 = 16 = 8 + 8 = 8 + √64

Since a^2 < b^2 < c^2, we have:

a < b < c