Simplifying Radicals
Simplify the expression.
√(125x)
5√ (5x)
Rationalize the denominator.
5 / √(3)
5√(3) / 3
Solve for x. Check if your answer is extraneous or not.
√(2x) = 4
x = 8
non extraneous
Complete the following operation. Write your result as in general form. (a + bi)
(9+2i) + (5-3i)
14 - i
Simplify.
√(20)
2√5
Simplify the expression.
√(-225)
15i
Rationalize the denominator.
√(x/5)
√(5x) / 5
Solve for x. Check if your solution is extraneous.
√(2x+3) - 3 = -2
x = -1
non-extraneous
Complete the following operation. Write your result as in general form. (a + bi)
(13-17i) - (9-14i)
4 - 3i
Simplify.
√(-16)
4i
Simplify the expression.
2 √(147x3y3)
14xy √(3xy)
Rationalize the denominator. Don't forget to simplify. (hint: i2= -1)
1 / (3-i)
3+i / 10
Solve for n. Check if you solution is extraneous.
√(3n) = √(4n − 1)
n = 1
non extraneous
Complete the following operation. Write your result as in general form. (a + bi)
3i (2 - i)
3 + 6i
Simplify.
i16
-1
Simplify the expression.
∛(64x14y6)
4x4y2 ∛ (x2)
Rationalize the denominator.
5 / (5 - √2)
(10 + 2√2) / 23
Solve for n. Check if you answer is extraneous or not.
n − 7 = √(3n − 21)
x = 7 and 10
Both are non extraneous
Complete the following operation. Write your result as in general form. (a + bi)
(7+3i)(5-2i)
41+i
Simplify.
i34
-1
Simplify the expression.
√(64x2/16y3)
(2x) / (y√ (y))
or
(2x√ y) / (y2)
Rationalize the denominator. Don't forget to simplify. (hint: i2= -1)
(1+3i) / (2+i)
1+ i
Solve for m. Check if your solutions are extraneous.
4 + √(-3m + 10) = m
No solution both answers are extraneous.
m = 3 and 2
Complete the following operation. Write your result as in general form. (a + bi)
(2 - 5i)2
-21-20i
Simplify.
i1485687
-i