If sqrt x = 25, then x^3 – x^2 = ?

[bhumika.k.shah]

If sqrt x = 25, then x^3 - x^2 = ?

A. 5^12
B. 5^20
C. 6(5^5)
D. 5^4(5^2 + 1)
E. 5^8(5^4 minus 1)

OA E

I got the answer but after literally multiplying 625^3-625^ and then solving each of the answer options
it was toooo time consuming

I would like to know a quicker approach.

Thanks

[apuso]

Below way of solving is an option:

x^3 - x^2
= (625)^3 - (625)^2
= (625)^2 ((625) - 1 )
= (5^4)^2 ((5^4)-1)
= (5^8) ((5^4) - 1)

[amittilak]

Given: sqrt x = 25,
which equals to, sqrt (x) = 5^2 (you have to realize after looking at the answer choices that you need to find the value in terms of 5)
hence, x = 5 ^4
and x^2 = 5^8
Now, lets look at what was asked:
x^3 - x^2 = ??
Simplifying,
x^3 - x^2 = x^2 (x - 1)
= 5^8 (5^4 - 1), which happens to be answer choice E.

[GMATinsight]

If sqrt x = 25, then x^3 - x^2 = ?

A. 5^12
B. 5^20
C. 6(5^5)
D. 5^4(5^2 + 1)
E. 5^8(5^4 minus 1)

OA E

I got the answer but after literally multiplying 625^3-625^ and then solving each of the answer options
it was toooo time consuming

I would like to know a quicker approach.

Thanks

Answer: Option D

Check solution

[melguy]

√x = 25
x = 25 x 25 (i.e. 5�)

Rephrase
What is 5� x 5� x 5� - 5� x 5�

Take 5� x 5� common
5� x 5� (5� - 1)
5^8 (5� - 1)

Answer is E

[Brent@GMATPrepNow]

If √x = 25, then x³ - x² = ?

A. 5¹²
B. 5²�
C. 6(5�)
D. 5�(5² + 1)
E. 5�(5� - 1)

If √x = 25, then x = 625
Or we can say that x = 25²
Since 25 = 5², we can say that x = 25² = (5²)² = 5�

So, x³ - x² = (5�)³ - (5�)²
= 5¹² - 5�
= 5�(5� - 1) [we factored out the greatest common factor]
= E

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[Matt@VeritasPrep]

I'd start with factoring:

x³ - x² =

x² * (x - 1)

Then plug in x = 625:

625² * 624

or

5� * (5� - 1)

[Jeff@TargetTestPrep]

If √x = 25, then x^3 - x^2 = ?

A. 5^12
B. 5^20
C. 6(5^5)
D. 5^4(5^2 + 1)
E. 5^8(5^4 - 1)

OA E

We start by squaring both sides of the equation √x = 25 to get:

x = 25^2 = (5^2)^2 = 5^4

We need to determine the value of x^3 - x^2, thus:

x^3 = (5^4)^3 = 5^12

x^2 = (5^4)^2 = 5^8

Thus:

x^3 - x^2 = 5^12 - 5^8 = 5^8(5^4 - 1)

Answer:E