Simplifying Radicals + Operations With Radicals

Simplifying

100

√64

8

200

2√196

28

300

√324

18

400

√72

6√2

500

5√200

50√2

Adding + Subtracting

100

√75 + √12

7√3

200

8√32 - 4√8

24√2

300

9√12 + √32 - √72

18√3 - 2√2

400

4√3 - √24 - √3

0

500

Find the perimeter of a square with side length of 3√52 + 7√32 feet

24√13 + 112√2 feet

Multipling

100

2√3 ⋅ 3√8

12√6

200

√3(4√2-√3)

4√6 - 3

300

(2+√5)(3-√5)

1 + √5

400

(√6-√7)²

13 - 2√42

500

Find the area of a rectangle with a width of 4√8 - 2√5 meters and a length of 4√8 + 2√5 meters.

108 meters squared

Variables

100

√45x⁴y³z

3x²y√5yz

200

√144x⁷y³¹

12x³y¹⁵√xy

300

3√4x² + 4√18x - 5√2x - 7x

7√2x - x

400

2√3(4√3x - 5√6x³)

24√x - 10x²√2x

500

(5√3x⁶y² - 9√y⁴) (5√3x⁶y^y + 9√y⁴)

75x⁶y² + 81y⁴

Rationalizing

100

(2√5) / (√3)

(2√15)/3

200

(√3 - 3) / (√20)

(√15 - 3√5) / 10

300

2 / (2√5 - 4)

√5 + 2

400

(3 + 2√3) / (2 + 2√3)

(3 + √3) / 4

500

(5 - 4√5) / (5 + √5)

(9 - 5√5) / 4