by: Bunuel
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by: Bunuel
34 mins
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Difficulty:
75%
(hard)
Question Stats:
55% (02:03) correct
45%
(02:08)
wrong
based on 408
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
_________________
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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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.
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.
Bunuel
\(\sqrt(\frac{8}{10})- \sqrt( \frac{1}{10})\)
\(=\frac{2 \sqrt(3)}{ \sqrt(2)\sqrt(5)}-\frac{1}{\sqrt(2)\sqrt(5)}\)
\(=\frac{2\sqrt(3) -1}{\sqrt(2)\sqrt(5)}\)
\(=\frac{\sqrt(2)\sqrt(3) -1}{\sqrt(5)} = \frac{\sqrt(6) -1}{\sqrt(5)}\)
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.
_________________
- Stne
General Discussion
stne
Why have we taken root of 8 as 2 root 3? Should it not be 2 root 2?
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
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
ridbag
Yes, you are correct. It should have been \(2\sqrt{2}\). Goofed up on this one. Thanks for pointing this out.
_________________
- Stne
I assumed x = √0.8 - √0.1 and squaed both sides. Seems to be an easier way to solve this.
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.
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
√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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