GMAT Quant Chapter 4: Roots & Exponents

Question 1

Which is the only number that has 1 square root and what is it?

Answer 1

0. The square root of 0 is 0

Question 2

Which is the only number that has 1 square root and what is it?

Answer 2

0. The square root of 0 is 0.

Question 3

What is the solution when a radical is used?
What is the solution to a number squared under a radical

Answer 3

only the nonnegative square root (principal root)
the absolute variable of the value, either + or -

Question 4

What must be true about the solution when the power of x and the index of a radical are both even

Answer 4

The root of x to the power n must be positive

Question 5

Does the GMAT consider 0 to be positive or negative?

Answer 5

Neither.

Links to another section of the Quant course.

Question 6

What are the first 11 nonnegative perfect cubes?

Answer 6

0
1
8
27
64
125
216
343
512
729
1000

Question 7

How do we find the solution to uncommon radicals?

Answer 7

Approximate the answer by judging the distance between the square roots of square numbers.

e.g. Root 7 is between root 9 = 3 and root 4 = 2 so around 2.7

Question 8

What kind of radicals can we never combine?

Answer 8

Those with different index numbers (how many times that exponent is repeated)

Question 9

On the GMAT what must we always do to radicals in the denominator of a fraction?

Answer 9

Move them to the top of the fraction by multiplying both sides by that radical

Question 10

How do we simplify a numerator with a radical if it has more than one term?

Answer 10

Create a conjugate pair
e.g if we have A + B, then we multiply that by A - B

Question 11

How do we calculate the solution to a binomial (more than one term) to an even power that is under a radical?

Answer 11

Results in an absolute value. We must plug the solution back into the original equation to see if it is correct. Do this when you have multiple solutions for x.

Question 12

In what cases when the bases on each side are equal are the exponents not equal?

Answer 12

1, -1, 0

Question 13

How do we simplify different bases that share the same exponent? (same with division)

Answer 13

Keep the common exponent and multiply the bases

Question 14

How do we convert a fractional base with a negative exponent?

Answer 14

Flip the fraction and make the exponent positive

Question 15

What do we do to the EXPONENTS when we multiply the bases?

Answer 15

Multiply the bases & add the exponents.

Question 16

If 0 < x < 1, what must be true?

Answer 16

x squared < x < root x

Question 17

When we are given two different numbers written in scientific notation, how can we compute the result?

Answer 17

Multiply the coefficients.
Multiply the exponent power of ten.
Combine both calculations seperately.

Question 18

When a perfect square has an even amount of trailing 0s, what will the square root be?

When a perfect cube has a number of trailing 0s that is divisible by 3, what will the cube root be?

Answer 18

The root of the perfect square plus half the number of trailing 0s

The cube root of that number plus 1/3 of the trailing zeros.

Question 19

What happens when we square decimal places?

Answer 19

We have double the amount of 0s before the first non-digit.

Question 20

How should we compare radicals and exponents?

Answer 20

raise numbers with big exponents to the reciprocal of the GCF (divide by the GCF and compare the resultant scaled numbers)

Question 21

What does B Root x to the power a correspond to in exponential form?

Answer 21

x to the power a/b