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

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)

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.

bhumika.k.shah wrote: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

√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

bhumika.k.shah wrote: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 RELATED VIDEOS - Laws of exponents – part I: https://www.gmatprepnow.com/module/gmat ... video/1025 - Greatest common factor factoring: https://www.gmatprepnow.com/module/gmat ... /video/954

I'd start with factoring: x³ - x² = x² * (x - 1) Then plug in x = 625: 625² * 624 or 5� * (5� - 1)

bhumika.k.shah wrote: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

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