Hello
How can i do the problem below in a faster way/shortcut:
Organize the following numbers from lowest to biggest:
-√5/5 , -√7/7 , -5/√5 , -7/√7 , -1
question on number properties with square roots
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Let us ignore the minus sign as of now.amyhussein wrote:Organize the following numbers from lowest to biggest:
-√5/5 , -√7/7 , -5/√5 , -7/√7 , -1
√5/5 = 1/√5 < 1
√7/7 = 1/√7 < 1
5/√5 = √5 > 1
7/√7 = √7 > 1
Now, √5 < √7 ---> 1/√5 > 1/√7
Hence, 1/√7 < 1/√5 < 1 < √5 < √7
Now, we'll introduce the minus signs, i.e. we'll multiply each of them with -1.
Hence, the order will get reversed.
Hence, required order ---> -7/√7 < -5/√5 < -1 < -√5/5 < -√7/7
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will the numbers relation for such type of problems still work if we square them all ? then add the -ve sign, so its easier to deal with solid numbers than roots?
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To organize the values in the correct order, we need to determine their RELATIVE distances from 0.amyhussein wrote:Hello
How can i do the problem below in a faster way/shortcut:
Organize the following numbers from lowest to biggest:
-√5/5 , -√7/7 , -5/√5 , -7/√7 , -1
Since all of the values are negative, the GREATER the distance from 0, the SMALLER the value.
To determine the relative distances, square all of the values and retain the negative signs:
-√5/5 --> -(√5/5)² = -1/5
-√7/7 --> -(√7/7)² = -1/7
-5/√5 --> -(5/√5)² = -5
-7/√7 --> -(7/√7)² = -7
-1 --> -(1²) = -1
The least value = the value furthest from 0 = -7/√7.
The greatest value = the value closest to 0 = -√7/7.
From least to greatest:
-7/√7, -5/√5, -1, -√5/5, -√7/7.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
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