Roots and Irrational Numbers Unit Test

Question

Math 8 Q2 (Pre-Algebra) / Roots and Irrational Numbers

simplify √48

Answer 1

To simplify √48, you can factor it into its prime factors.

Start by finding the perfect square factor of 48. The largest perfect square that divides 48 is 16 (4^2).

Divide 48 by 16 to get 48/16 = 3.

Now, express 16 as the product of its prime factors: 16 = 2^4.

Simplify the square root of 48 as follows:

√48 = √(16 * 3)

Using the product property of square roots, you can split the square root into the product of two separate square roots:

√48 = √16 * √3

Simplify both square roots:

√16 = 4

√3 remains the same.

Therefore, √48 = 4√3.