IF P = 9^{1/2} - 9^{1/3} - 9^{1/4}, then P is:

Question

If  P = 9^{\frac{1}{2}} - 9^{\frac{1}{3}} - 9^{\frac{1}{4}} , then P is:

A) Less than 0

B) Equal to 0

C) Between 0 and 2

D) Between 2 and 3

E) Greater than 3

PyjamaScientist · Answer

\sqrt{9} = 3

9^\frac{1}{3} = 2.x . Since,  9^\frac{1}{3}  is greater than  8^\frac{1}{3}

9^\frac{1}{4}  would be greater than 1. Since,  9^\frac{1}{4}  is greater than  1^\frac{1}{4} 
 
So, 3 - 2.x - 1.y => 0.x - 1y. The result has to be negative. Thus < 0.

shubhim20 · Answer

could you please explain this in detail

Krunaal · Answer

P = 9^{1/2} - 9^{1/3} - 9^{1/4}

9^\frac{1}{2} = 3

Now we are subtracting two values from  3 , viz.  9^{1/3}  and  9^{1/4}

9^{1/3}  => it is difficult to calculate this, so we try to approximate a value. We know that  cube root of 8 is 2 , therefore  cube root of 9 must be greater than 2

Again,  9^{1/4}  => difficult to calculate fourth root, so we approximate.  Fourth root of 1 is 1, so fourth root of 9 must be greater than 1

Now, to find P,  we will subtract something greater than 2, and something greater than 1 from 3

P = 3 - something greater than 2 - something greater than 1
P = 3 - (something greater than 2 + something greater than 1)
P = 3 - (something greater than 3) =>  P is negative

Hope it is clear.

IF P = 9^{1/2} - 9^{1/3} - 9^{1/4}, then P is:

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IF P = 9^{1/2} - 9^{1/3} - 9^{1/4}, then P is:

Prep Toolkit

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