Question

square root of 48 as product of integer and irrational square root

Answer 1

To express the square root of 48 as a product of an integer and an irrational square root, we can start by simplifying \( \sqrt{48} \).

First, we can factor 48 into its prime factors:
\[
48 = 16 \times 3
\]
Next, we can take the square root of 16, as it is a perfect square:
\[
\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3}
\]

Since \( \sqrt{16} = 4 \), we have:
\[
\sqrt{48} = 4 \times \sqrt{3}
\]

Thus, the square root of 48 expressed as a product of an integer and an irrational square root is:
\[
\sqrt{48} = 4\sqrt{3}
\]