cube root

[swapna]

Can some body suggest an easy way to find cube root of a number??

Swapna

[KapTeacherEli]

Hi swapna,

On the GMAT, you never should need to.

The basic cube roots you should simply memorize; 2, 3, 4, and 5 cubed (8, 27, 64, and 125) are about as large as you are likely to see and still be expected to actually get a numerical value. In nearly ever other case on the GMAT, the cube root will either A) cancel out with a cube elsewhere in the equation, B) be listed as a cube root in the answer choices so there is no need to solve, or C) be part of a Data Sufficiency question where you don't need a numerical value to answer correctly.

That being said, if you really, really need to know if a big number is a perfect cube, the best way to do so is with a Factor Tree to break down the number into its prime factorization.

For instance, 216 = 2 x 108 = 2 x 2 x 54 = 2 x 2 x 2 x 27 = 2 x 2 x 2 x 3 x 9 = 2 x 2 x 2 x 3 x 3 x 3 = 6^3. But as you can see, this is clunky; it should be used only as a last resort.

[bedazzled]

Hi swapna,

You can actually post the question in which u confronted cube roots. So, we can see is there any easier way or not. Thanx Eli Meyer for ur explanation.

[swapna]

yeah....i guess...i will try pullin up the question....thanks

[swapna]

What is the cube root of w ?
(1) The 5th root of w is 64.
(2) The 15th root of w is 4.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

The answer is D

[regor60]

What is the cube root of w ?
(1) The 5th root of w is 64.
(2) The 15th root of w is 4.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

The answer is D

This is solved by recognizing that 64 = 4^3 and proceeding from there to recognize that statement 1 is equivalent to statement 2...

[swapna]

hi...thanks...but could u please elaborate on that a bit....

[KapTeacherEli]

Actually, the key here is recognizing that roots are, by definition, positive; they only have one solution. That means as soon as we know the 5th root of w is a number, it doesn't matter what that number is; w will always, always have exactly one solution.

[varchar]

(1) The 5th root of w is 64. => w^1/5 = 64; so w=64^5
(2) The 15th root of w is 4. => w^/15 = 4; so w =4^15 => w = (4^3)^5 => 64^5

Ans: D

[money9111]

someone correct me if I'm wrong but you don't even need to calculate anything...

the question is "What is the cube root of W ?" another way of saying this is "What is W" or "Find W" because if we know W then we know would be able to find the cube root...

statement 1) we know we can find W since they give us an equation w/ 1 variable (W) = sufficient
statement 2) we know we can find W since they give us a different equation w/ 1 variable (W) = sufficient

both are sufficient so D is correct...

[KapTeacherEli]

someone correct me if I'm wrong but you don't even need to calculate anything...

the question is "What is the cube root of W ?" another way of saying this is "What is W" or "Find W" because if we know W then we know would be able to find the cube root...

statement 1) we know we can find W since they give us an equation w/ 1 variable (W) = sufficient
statement 2) we know we can find W since they give us a different equation w/ 1 variable (W) = sufficient

both are sufficient so D is correct...

Be careful about the "one equation, one variable" rule. Various things--squares, absolute values, inequalties, variables that cancel with themselves--can result in the rule not applying. However, in this specific case you're absolutely correct. Roots only have one solution (they're always positive by definition), and so a single-variable equation will always have one solution. Actual solving is unnecessary.

[money9111]

I actually made a notecard about being careful about this... that's the only reason I was able do solve it that way... honestly though, had I taken the test today... and seen that question.. i would have blanked out - forgotten my notes - and gotten it wrong :-/