Discussion
| Column A | Column B | |
|---|---|---|
| The square root of 7/8 | The square of 7/8 |
| (A) | Column A is larger |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 05/22/2013 20:01
Couldn't the square root of 7/8 be negative, therefore making it smaller than the square of 7/8?
Posted: 05/22/2013 21:16
Hi Charlotte,
When we are given a square root, it is always positive, and is called the principal root. When we introduce at root by, say, solving an equation, then we have to consider both the positive root and the negative root.
For example, we solve the equation x^2 = 4 by taking the square root of both sides of the equation, which yields
x = 2 and -x = 2 (A)
or
x = 2 and x = -2 (B)
Notice that in Step (A) we put the negative with the x, not with the 2. When solving equations like this one, Step (A) is usually not shown. We are showing it here to illustrate that it is the x that can be negative, not the 2. The 2 is the principal root of 4, which is always positive.
Thus, the square root of 7/8 is the principal root of 7/8, and it is positive.
Nova Press
When we are given a square root, it is always positive, and is called the principal root. When we introduce at root by, say, solving an equation, then we have to consider both the positive root and the negative root.
For example, we solve the equation x^2 = 4 by taking the square root of both sides of the equation, which yields
x = 2 and -x = 2 (A)
or
x = 2 and x = -2 (B)
Notice that in Step (A) we put the negative with the x, not with the 2. When solving equations like this one, Step (A) is usually not shown. We are showing it here to illustrate that it is the x that can be negative, not the 2. The 2 is the principal root of 4, which is always positive.
Thus, the square root of 7/8 is the principal root of 7/8, and it is positive.
Nova Press
Posted: 05/22/2013 23:01
Thank you! Very helpful.
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