Radical equations

Simplify

100

√144

12

200

√(4x²

2x

300

√50

5√2 

400

√72x⁴y²

6x²y√2

500

3√8x⁶ - √18x²

6x³-3x√2

Solve

100

√x=5

25

200

√(x+3)=6

33

300

√(2x-1) = 3

x=5

400

√(x+2) +1 = 5

x=14

500

√(x+4) = x-2

x=4

x≠-1 (extraneous)

Extraneous or not?!

100

√x=-5

Extraneous!

For this equation, the answer is x=25. But, if you plug 25 in to the equation, you get √25=-5 which is not a true statement. 

200

√(x+6)=4

Not extraneous!

x=10

300

√(x+2)=-3

Extraneous!

For this equation, you would get x=7, but when you plug that back into the equation, you get that √9=-3 which is not true.

400

√(x+4)=x-2

x=5

x≠0

500

√(x+7) = x-1

this is a tricky one🙈 Remember the quadratic formula!

x≠3/2-1/2√33

x=3/2+1/2√33

Radical Riddles

100

What is the square root of 1/4?

1/2

200

I am a number. When you add 7 to me, then take the square root, the result is 5. What number am I?

x=18

300

A square has an area of 128. What is the side length?

8√2

400

a square garden has an area equal to √256.

Find a side length!

4

500

I am painting a square canvas. One side length of this canvas is √3x+1 feet. The perimeter of the canvas is 36 feet. Find x

80/3

Mix and Match

100

√36+√64

14

200

Solve. √(x²-1) = 4

x=+-√17

(plus minus)

300

(√18)(√2)

6

400

√(x+5)=√(3x-1)

x=3

500

Simplify: 2√3+√2

Trick Question!

It is already simplified!