Square Roots and Exponents

Square Roots (perfect squares)

100

What is the positive square root of 121?

11

200

What is the negative square root of 64?

-8

300

What are the positive and negative square roots of 100?

10 and -10

400

What is the square root of -36?

-36 has NO square root

500

What is the negative square root of 144?

-12

Simplifying Square Roots

100

The square root of 12

2 * Square root 3

200

The square root of 48

4 * Square root of 3

300

The square root of 25/36

5/6

400

The square root of 18/49

(3 * square root of 2) / 7

500

x = -2, y = 8, z = 1/2

Simplify: The square root of (y - 44xz)

2 * Square root of 13

Multiplying with Exponents

100

d^5 * d^10

d^15

200

3x^7 * 4x^8

12x^15

300

12y^11 * 6y^20

72y^31

400

10a^4b^11 * 3a^3b^2

30a^7b^13

500

6x^4y^10z^11 * 7x^12y^3z^14

42x^16y^13z^25

Dividing with Exponents

100

b^10 / b^2

b^8

200

a^10b^14 / a^4b^8

a^6b^6

300

12x^12 / 8x^4

3x^8 / 2

400

45y^3 / 25y^9

9 / 5y^6

500

36x^3y^10 / 60x^8y^7

3y^3 / 5x^5

Multiplying/Dividing with Exponents Mix

100

3y^14 * 8y

24y^15

200

120b^11 / 50b^3

12b^8 / 5

300

6a^4b^9 * 16a^12b^11

96a^16b^20

400

10a^3b^2 / 40a^9b^5

1 / a^6b^3

500

12x^8y^11 / 28x^3y^15

3x^5 / 7y^4