Converting to Mixed Radicals
Simplify the following radical:
sqrt(144)
12
Write as a whole radical:
2sqrt(10)
sqrt(40)
Simplify:
2root(3)(7)+4root(3)(7)
6root(3)(7)
Multiply and simplify if possible:
sqrt(6)*sqrt(3)
3sqrt(2)
Rationalize the denominator:
sqrt(11)/sqrt(2)
sqrt(22)/2
Simplify the following radical:
root(3)(54)
3root(3)(2)
Write as a whole radical:
5sqrt(3x)
sqrt(75x)
Simplify:
-3sqrt(5)+2sqrt(5)
-1sqrt(5)
Multiply and simplify if possible:
3sqrt(8)*sqrt(2)
12
Rationalize the denominator:
sqrt(10)/(2sqrt(3))
sqrt(30)/6
Simplify the following radical:
root(3)(16b^4)
2broot(3)(2b)
Write as a whole radical:
3root(3)(10)
root(3)(270)
Simplify:
sqrt(3)+sqrt(12)
3sqrt(3)
Multiply and simplify if possible:
5sqrt(3)*2sqrt(6)
30sqrt(2)
Rationalize the denominator:
(4+sqrt(2))/sqrt(5)
(4sqrt(5)+sqrt(10))/5
Simplify the following radical:
2sqrt(72m^4n^3)
12m^2nsqrt(2n)
Write as a whole radical:
4mroot(3)(2)
root(3)(128m^3)
Simplify the following radicals:
5sqrt(90)+2sqrt(160)
23sqrt(10)
Multiply and simplify if possible:
sqrt(2x^2)*sqrt(10x^3)
2x^2sqrt(5x)
Rationalize the denominator:
(sqrt(7))/(3+sqrt(6))
(3sqrt(7)-sqrt(42))/3
Simplify the following radical:
sqrt(12x^4y^3z^2)
2x^2yz sqrt(3y)
Write as a whole radical:
2xy^3sqrt(3)
sqrt(12x^2y^6)
Simplify the following radicals:
-2sqrt(72)-3sqrt(24)+2sqrt(128)
4sqrt(2)-6sqrt(6)
Multiply and simplify if possible:
(sqrt(5)+3sqrt(2))(2sqrt(5)-sqrt(2))
4+5sqrt(10)
Rationalize the denominator:
(sqrt(2)+2sqrt(3))/(2sqrt(5)-sqrt(3))
(2sqrt(10)+sqrt(6)+4sqrt(15)+6)/17