Simplifying a Radical (Part 1)

Simplifying a Radical (Part 1)

How to simplify a radical (Part 1): examples and their solutions.

Example 1

Simplify the given expression. (x > 0) sqrt(4x^2)

Make the factors of the radicand
in squared form:
22, x2

Then the square root and the square are cancelled.
And the bases (2, x) can get out from the radical sign.

Example 2

Simplify the given expression. (a, b, c > 0) sqrt(5(a^2)b(c^4))

Make the factors of the radicand
in squared form:
a2, (c2)2

Then the square root and the square are cancelled.
And the bases (a, c2) can get out from the radical sign.

Example 3

Simplify the given expression. (k > 0) sqrt(12k^7)

To make the squared form:

Change 12 to 22⋅3
(prime factorization)

Change k7 to k6k.
(make an even power: 6)

Make the factors of the radicand
in squared form:
22, (k3)2

Then the square root and the square are cancelled.
And the bases (2, k3) can get out from the radical sign.