Simplifying a Radical (Part 2)

Simplifying a Radical (Part 2)

How to simplify a radical (Part 2): examples and their solutions.

Example 1

Simplify the given expression. Square root (18(x^4)(y^7)).

Factor 18: 2⋅32.

Divide each factor's power by 2 (square root).
Write the powers as (quotient)⋅2 + (remainder).
32 = 31⋅2
x4 = x2⋅2
y7 = y3⋅2 + 1

Make square forms.
31⋅2 = 32
x2⋅2 = (x2)2
y3⋅2 + 1 = (y3)2y

Take the available base parts
out from the radical sign:
3, x2, and y3.

For y3, add an absolute value sign: |y3|

nth root of a number

Simplifying a radical (part 1)

Example 2

Simplify the given expression. Cube root (16(x^5)(y^9))

Factor 16: 24.

Divide each factor's power by 3 (cube root).
Write the powers as (quotient)⋅3 + (remainder).
24 = 21⋅3 + 1
x5 = x1⋅3 + 2
y9 = y3⋅3 + 0

Make square forms.
21⋅3 + 1 = 23⋅2
x1⋅3 + 2 = x3x2
y3⋅3 + 0 = (y3)3

Take the available base parts
out from the radical sign:
2, x, and y3.

nth root of a number