Simplifying Radicals
Simplify.
2\sqrt144
24
When you are adding and subtracting radicals, what must be the same?
The radicand/number on the inside AND the nth (square root, cube, fourth,...)
Express in simplest radical form.
sqrt6 * 7sqrt30
42sqrt5
When converting a radical to exponential form, where does the denominator come from?
The nth. So when its a square root the denominator is 2, when its a cube root the denominator is 3, and so on.
a) To add or sub fractions what must be true?
b) Does it have to be true when multiplying and dividing?
a) the denominators have to be the same.
b) no.
Simplify.
root3(c^9)
c^3
Expres
4sqrt6 + 10 sqrt6
s in simplest form.
14sqrt6
Express in simplest radical form.
10 * root3(375)
50root3(3)
Write the expression in exponential form.
root5(x^2)
x^(2/5)
Perform the operation and simplify the answer fully.
(1/6)/-3
-1/18
Simplify.
4root4(2401x^9)
28x^2root4(x)
Express in simplest radical form.
13sqrt64 - 8sqrt64
40
Write the following expression in simplest radical form.
(sqrt(m^6))(sqrt(32m^3))
4m^5sqrt(2m)
Write the expression in radical form.
x^(3/5)
root5(x^3)
Perform the operation and simplify the answer fully.
(5/6+1/15)/(2/5
9/4
Simplify.
4x^3 sqrt(28x^7y^6)
8x^6y^3sqrt7
Express in simplest radical form.
-sqrt45 + 3sqrt20
3sqrt5
Express in the simplest form.
(sqrt250)/5
sqrt10
express in simplest radical form.
(4^(1/3))^4
4root3(4)
perform the operation and simplify the answer fully.
(2/3)/(7/5 - 12/7)
-70/33
Simplify.
x^3y^2 root3(24x^5y^6)
2x^4y^4 root3(3x^2)
Express in simplest radical form.
-5root3(24) + root3(81)
-7root3(3)
Express in simplest radical form with a rational denominator.
(sqrt(96x^10))/(sqrt(6x))
4x^4sqrt(x)
Convert to simplest radical form.
1/ (2x+7)^(1/2)
1/ sqrt(2x +7)
(1/6 +2/15)/ (4/7)
21/40