The value of −3 + √(9−k) is positive for which of the following values

Question

The value of  −3 + \sqrt{9−k}  is positive for which of the following values of k ?

I. -1
II. 0
III. 1

A. None
B. I only
C. II only
D. III only
E. I and III

KarishmaB · Accepted Answer

Given Expression =  -3 + \sqrt{9 - k} 
If k = 1
Given Expression =  -3 + \sqrt{8} 
We know that  \sqrt{9} = 3 . So  \sqrt{8}  will be a little less than 3.
Given Expression = -3 + Something less than 3 = A little negative quantity

If k = 0
Given Expression =  -3 + \sqrt{9} 
Given Expression =  -3 + 3  = 0 = A non-negative non-positive quantity

If k = -1
Given Expression =  -3 + \sqrt{10} 
We know that  \sqrt{9} = 3 . So  \sqrt{10}  will be a little more than 3.
Given Expression = -3 + Something more than 3 = A little positive quantity

It is positive only for k = -1

Answer B.

Skywalker18 · Answer

For the expression to be positive ,  \sqrt{9−k}  should return a value greater than 3
It will be true only when k<0
=> k=-1

Answer B

niks18 · Answer

As per the question  −3 + \sqrt{9−k}>0  or  \sqrt{9−k}>3 . Squaring both sides we get
 9-k>9 . Hence  k<0 . From the given values only  -1  satisfies this condition

Option  B

JeffTargetTestPrep · Answer

We can analyze each Roman numeral:

I. -1

-3 + √(9 - (-1))

-3 + √10

-3 + 3.2 is positive.

II. 0

-3 + √(9 - 0)

-3 + √9

-3 + 3 is NOT positive.

III. 1

-3 + √(9 - 1)

-3 + √8

-3 + 2.8 is NOT positive.

Alternate Solution:

-3 + √(9 - k) > 0

√(9 - k) > 3

9 - k > 9

-k > 0

k < 0

Of the choices, only Roman numeral I, for which k = -1, satisfies the requirement for the value of k.

Answer: B

vp101 · Answer

I have a doubt.

In each of the cases whether we consider the value whose square root we are taking as 9, 10, or 8, can't the actual square root be either positive or negative? As a result, we cannot ascertain whether any of the values from amongst the options given (-1, 0, or +1) will for sure provide an end result that is a positive number.

Is there something I am missing here?

priancagupt · Answer

B 
The number is negative when k is 0 or greater than 1. 
K has to be negative.

Posted from my mobile device

bumpbot · Answer

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The value of −3 + √(9−k) is positive for which of the following values

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The value of −3 + √(9−k) is positive for which of the following values

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