Roots and Radicals Quiz

List the perfect squares, cubes, and fourths.

Answer explanation

List the perfect squares, cubes, and fourths by finding the numbers that are the result of multiplying a number by itself (squares), by itself three times (cubes), and by itself four times (fourths).

____ and ____ are square roots of 81 because __________ and __________

Answer explanation

9 and -9 are square roots of 81 because 9 * 9 = 81 and -9 * -9 = 81

____ is the cube root of -8 because __________

Answer explanation

The cube root of -8 is -2 because -2 * -2 * -2 = -8, as multiplying three -2s gives -8.

____ and ____ are fourth roots of 256 because __________ and __________

Answer explanation

16 and -16 are fourth roots of 256 because 16^4 = 256 and (-16)^4 = 256

If there is no index, it is assumed that __________.

Answer explanation

If there is no index, it is assumed that the starting index is 0.

√16 = (a)  

Answer explanation

√16 = 4 because the square root of a number is the value that, when multiplied by itself, gives the original number. In this case, 4 * 4 = 16.

-√121 = (a)  

Answer explanation

The square root of 121 is 11. Since we have a negative sign in front of the square root, the answer is -11.

√289 = (a)  

Answer explanation

√289 = 17, as the square root of 289 is the number which when multiplied by itself gives 289.

-√4/25 = (a)  

Answer explanation

-√4/25 = -√(4)/√(25) = -2/5 = -0.4

∛8 = (a)  

Answer explanation

∛8 = 2 because 2 * 2 * 2 = 8. The cube root of 8 is 2.