Radical, Complex and Rational Expressions Review

Simplify

100

sqrt(18x^4y^3)

3x^2ysqrt(2x)

200

root(4)(112x^5y^8

2xy^2root(4)(7x)

300

frac(2x+6)(4x-12)

frac(x+3)(2(x-3)

400

frac(9x^2+18x+9)(3x+3)

3(x+1)

500

frac(3x^2+25x-18)(3x^2-23x+14)

frac(x+9)(x-7)

Addition

100

(3+2i)+(1-5i)

4-3i

200

frac(5)(x+5)+frac(7x)(x+5)

frac(5+7x)(x+5)

300

8root(4)243+root(4)48

26root(4)3

400

frac(x+2)(3)+frac(x-4)(4)

frac(7x-4)(12)

500

frac(x+3)(x-2)+frac(x-3)(x+1)

frac(2x^2-x+9)((x+1)(x-2)

Subtraction

100

(4-2i)-(6-7i)

-2+5i

200

frac(4x^2)(x-5)-frac(-2)(x-5)

frac(4x^2+2)(x-5)

300

sqrt(27a^4b)-a^2sqrt(12b)

a^2sqrt(3b)

400

frac(4)(x+1)-frac(5)(x-3)

frac(-x-17)((x+1)(x-3)

500

frac(3x)(x+1)-frac(2x+5)(x-2)

frac(x^2-13x-5)((x+1)(x-2)

Multiplication

100

sqrt3(4+2sqrt7)

4sqrt3+2sqrt21

200

sqrt(-2)(sqrt(-18)+7)

-6+7isqrt2

300

(3-4i)(5+2i)

23-14i

400

frac(24x^3)(50x)xxfrac(30)(8x^2)

frac(9)(5)

500

frac(6x-12)(x^2-9x+18)xxfrac(7x-21)(5x-10)

frac(42)(5(x-6)

Division

100

frac(2sqrt3)(7sqrt5)

frac(2sqrt15)(35)

200

frac(sqrt50-sqrt8)(sqrt2)

3

300

frac(x^2-49)(x^2-4x-12)-:frac(3x-21)(9x+18)

frac(3(x+7))(x-6)

400

frac(3+2i)(4-5i)

frac(2+23i)(41)

500

frac(frac(m+4)(m^2)+frac(m-5)(m^2))(m-5

frac(2m-1)(m^3-5m^2) OR frac(2m-1)(m^2(m-5))