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Bunuel
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The approximation of 0.8 - 0.1 is between? 07 Jun 2023, 11:00
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

53% (02:04) correct 47% (02:17) wrong based on 260 sessions

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The approximation of √0.8 - √0.1 is between?

A. 1/5 and 1/4
B. 1/4 and 1/3
C. 1/3 and 1/2
D. 1/2 and 2/3
E. 2/3 and 1
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D
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stne
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The approximation of 0.8 - 0.1 is between? 10 Jun 2023, 09:59
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Bunuel
The approximation of √0.8 - √0.1 is between?

A. 1/5 and 1/4
B. 1/4 and 1/3
C. 1/3 and 1/2
D. 1/2 and 2/3
E. 2/3 and 1

\(\sqrt(\frac{8}{10})- \sqrt( \frac{1}{10})\)

\(=\frac{2 \sqrt(3)}{ \sqrt(2)\sqrt(5)}-\frac{1}{\sqrt(2)\sqrt(5)}\)

\(=\frac{2\sqrt(3) -1}{\sqrt(2)\sqrt(5)}\)

\(=\frac{\sqrt(2)\sqrt(3) -1}{\sqrt(5)} = \frac{\sqrt(6) -1}{\sqrt(5)}\)

We know \(2 <\sqrt{5}<3\) and also \(2<\sqrt{6} <3\) Hence \(\sqrt{5} \approx \sqrt{6}\)

Taking \(\sqrt{5} = 2\) and \(\sqrt{6} = 2\)

\(\frac{\sqrt(6) -1}{\sqrt(5)} = \frac{1}{2} \)

Taking \(\sqrt{5} = 3 \) and \(\sqrt{6} = 3\)

\(\frac{\sqrt(6) -1}{\sqrt(5)} = \frac{2}{3} \)

Therefore \(\frac{1}{2} < \frac{\sqrt(6) -1}{\sqrt(5)} < \frac{2}{3}\)

Ans D

Hope it helps.
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ridbag
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The approximation of 0.8 - 0.1 is between? 20 Jun 2024, 03:14
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stne
Bunuel
The approximation of √0.8 - √0.1 is between?

A. 1/5 and 1/4
B. 1/4 and 1/3
C. 1/3 and 1/2
D. 1/2 and 2/3
E. 2/3 and 1
\(\sqrt(\frac{8}{10})- \sqrt( \frac{1}{10})\)

\(=\frac{2 \sqrt(3)}{ \sqrt(2)\sqrt(5)}-\frac{1}{\sqrt(2)\sqrt(5)}\)

\(=\frac{2\sqrt(3) -1}{\sqrt(2)\sqrt(5)}\)

\(=\frac{\sqrt(2)\sqrt(3) -1}{\sqrt(5)} = \frac{\sqrt(6) -1}{\sqrt(5)}\)

We know \(2 <\sqrt{5}<3\) and also \(2<\sqrt{6} <3\) Hence \(\sqrt{5} \approx \sqrt{6}\)

Taking \(\sqrt{5} = 2\) and \(\sqrt{6} = 2\)

\(\frac{\sqrt(6) -1}{\sqrt(5)} = \frac{1}{2} \)

Taking \(\sqrt{5} = 3 \) and \(\sqrt{6} = 3\)

\(\frac{\sqrt(6) -1}{\sqrt(5)} = \frac{2}{3} \)

Therefore \(\frac{1}{2} < \frac{\sqrt(6) -1}{\sqrt(5)} < \frac{2}{3}\)

Ans D

Hope it helps.
­Why have we taken root of 8 as 2 root 3? Should it not be 2 root 2?
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The approximation of 0.8 - 0.1 is between? 20 Jun 2024, 06:22
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A quick way with a moderate risk of error is to recognize that √.8 is very close to but less than:

0.9

and that √.1 is very close to but greater than:

0.3

So the difference between the two is definitely less than:

.9-.3 = .6

However, it seems very likely:

>0.5, so D is a plausible answer

Posted from my mobile device
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stne
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The approximation of 0.8 - 0.1 is between? 21 Jun 2024, 14:46
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ridbag
stne
Bunuel
The approximation of √0.8 - √0.1 is between?

A. 1/5 and 1/4
B. 1/4 and 1/3
C. 1/3 and 1/2
D. 1/2 and 2/3
E. 2/3 and 1
\(\sqrt(\frac{8}{10})- \sqrt( \frac{1}{10})\)

\(=\frac{2 \sqrt(3)}{ \sqrt(2)\sqrt(5)}-\frac{1}{\sqrt(2)\sqrt(5)}\)

\(=\frac{2\sqrt(3) -1}{\sqrt(2)\sqrt(5)}\)

\(=\frac{\sqrt(2)\sqrt(3) -1}{\sqrt(5)} = \frac{\sqrt(6) -1}{\sqrt(5)}\)

We know \(2 <\sqrt{5}<3\) and also \(2<\sqrt{6} <3\) Hence \(\sqrt{5} \approx \sqrt{6}\)

Taking \(\sqrt{5} = 2\) and \(\sqrt{6} = 2\)

\(\frac{\sqrt(6) -1}{\sqrt(5)} = \frac{1}{2} \)

Taking \(\sqrt{5} = 3 \) and \(\sqrt{6} = 3\)

\(\frac{\sqrt(6) -1}{\sqrt(5)} = \frac{2}{3} \)

Therefore \(\frac{1}{2} < \frac{\sqrt(6) -1}{\sqrt(5)} < \frac{2}{3}\)

Ans D

Hope it helps.
­Why have we taken root of 8 as 2 root 3? Should it not be 2 root 2?
­Yes, you are correct. It should have been \(2\sqrt{2}\)­. Goofed up on this one. Thanks for pointing this out.
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The approximation of 0.8 - 0.1 is between? 22 Jun 2024, 03:44
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We are asked for an approximation so no need to calculate the exact value.

We can look for two values close to 0.8 and 0.1, for each of which we know the square root.

0.8 is close to 0.81 which has a square root of 0.9.
0.1 is close to 0.09 which has a square root of 0.3.

Hence,  √0.8 - √0.1 is approximately 0.6.

Answer is D.
 ­
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The approximation of 0.8 - 0.1 is between? 16 Feb 2025, 10:03
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I assumed x = √0.8 - √0.1 and squaed both sides. Seems to be an easier way to solve this.
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The approximation of 0.8 - 0.1 is between? 16 Feb 2025, 10:08
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Nice tricky question. I figured that 0.1 was close to 0.09, which is 0.3 squared, so this has to be between something that's slightly greater than 0.3 and slightly less than 0.3.
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The approximation of 0.8 - 0.1 is between? 16 Feb 2025, 11:26
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Another approach, close to the others but maybe a bit quicker

√0.8 = √(80/100) ≈ √(81/100) ≈ 9/10
√0.1 = √(10/100) ≈ √(9/100) ≈ 3/10

Hence, √0.8 - √0.1 ≈ 6/10

-> Answer D
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