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Which is greater 0.4 or \sqrt 0.4
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21 Feb 2019, 11:21
21 Feb 2019, 11:21
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Question Stats:
74% (00:23) correct
24% (00:22) wrong based on 112 sessions
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Quantity A |
Quantity B |
\(0.4\) |
\(\sqrt{0.4}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Re: Which is greater 0.4 or \sqrt 0.4
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21 Feb 2019, 12:12
21 Feb 2019, 12:12
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Carcass wrote:
Quantity A |
Quantity B |
\(0.4\) |
\(\sqrt{0.4}\) |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
CHALLENGE: Build your number sense skills by solving this one without using a calculator.
Let's examine some other roots:
√0.64 = 0.8 (since 0.8² = 0.64)
√0.49 = 0.7 (since 0.7² = 0.49)
√0.36 = 0.6 (since 0.6² = 0.36)
Since 0.4 is BETWEEN 0.36 and 0.49, we know that √0.4 is BETWEEN √0.36 and √0.49
In other words, √0.4 is BETWEEN 0.6 and 0.7
We get:
QUANTITY A: 0.4
QUANTITY B: some number between 0.6 and 0.7
Answer: B
Cheers,
Brent
General Discussion
Re: Which is greater 0.4 or \sqrt 0.4
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28 Feb 2019, 17:37
28 Feb 2019, 17:37
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Also handy to know is that when numbers greater than 1 are squared, they get bigger. When numbers between 0 and 1 are squared, they get smaller.
Similarly, the square root of numbers greater than 1 is less than the original number. The square root of numbers between 0 and 1 is greater than the original number.
This is because multiplying something by a fraction or decimal makes it smaller. So if x*x = 0.4, and x is a fraction or decimal, x will have to be larger than 0.4 in order to equal 0.4 when multiplied by itself.
Similarly, the square root of numbers greater than 1 is less than the original number. The square root of numbers between 0 and 1 is greater than the original number.
This is because multiplying something by a fraction or decimal makes it smaller. So if x*x = 0.4, and x is a fraction or decimal, x will have to be larger than 0.4 in order to equal 0.4 when multiplied by itself.
