Radicals

Perfect Squares

100

What is the square root of 64?

8

200

What is the square root of 25 plus the square root of 144?

17

300

What are the first 10 perfect squares?

1, 4, 9, 16, 25, 36, 49, 64, 81, 100

400

What is the cube root of 27?

3

500

What is the cube root of -64?

-4

Simplifying

100

Simplify √12 

2√3

200

Simplify √54

3√6

300

Simplify -3√28

-6√7

400

Simplify the following radical 4∛125

20

500

Simplify: ∛-48

-2∛6

Radical to Exponential

100

Convert to exponential form √x⁵

x^5/2

200

Convert to radical form 5^1/3 

³√5

300

Convert to exponential form (√75x³ )³

75^3/2x^9/2

400

Convert to radical form and simplify (3x²)^4/3

3³√3x⁴

500

Convert to radical form (7x²y³)^4/5

⁵√2401x⁸y¹²

Adding/Subtracting

100

In order to add radicals, which of the following must be true?

(a) The radicals must have the same index

(b) The radicals must have the same radicand

(c) The radicals must have the same number outside the radical sign

(d) Both a and b

d. both a and b

200

Add the following radicals: 4√3 + 2√3 + 7√3.

13√3

300

Subtract the following radicals: 6√5 - √125.

√5

400

Add the following radicals: √8 + √98 + √72.

15√2

500

Add/Subtract the following radicals: 7√18 + 2√25 - 3√72.

10 + 3√2

Multiplying

100

Generally speaking, in order to multiply radicals, which of the following must be true?

(a) The radicals must have the same index

(b) The radicals must have the same radicand

(c) The radicals must have the same number outside the radical sign

(d) Both a and b

a

200

Multiply the following radicals: √5 x √8. Simplify if necessary.

2√10

300

Multiply the following radicals: √10 times 3√20

30√2

400

What is the area of a square with side length 3√7 inches? 

63 inches²

500

Multiply the following radicals: 4√6(2√27-√18)

72√2-24√3