Products of Irrational Square Roots Practice

Question

Complete this assessment to review what you've learned. It will not count toward your grade.
4 of 54 of 5 Items
Question
What is 54−−√3
simplified?

Note: You will find the option to add a cubic root symbol in the Algebra (×)
keyboard.

(1 point)
Remaining Attempts : 3

Answer 1

To simplify the expression \(\sqrt{54} \cdot 3\), you can start by simplifying \(\sqrt{54}\).

1. Factor \(54\) into its prime factors: \[ 54 = 9 \times 6 = 3^2 \times 6 \]

2. Now, find the square root of \(54\) using the prime factorization: \[ \sqrt{54} = \sqrt{9 \times 6} = \sqrt{9} \cdot \sqrt{6} = 3\sqrt{6} \]

3. Now multiply that by \(3\): \[ \sqrt{54} \cdot 3 = 3\sqrt{6} \cdot 3 = 9\sqrt{6} \]

So, the expression \(\sqrt{54} \cdot 3\) simplified is \(9\sqrt{6}\).