Question 4 of 10 , Step 1 of 1
$2/10$
Correct
Simplify the following expression.
$$\sqrt{180}$$

Answer

Step 1 ：Simplify the following expression: $\sqrt{180}$

Step 2 ：To simplify the square root of 180, we need to find the prime factorization of 180 and pair the prime factors. The square root of a pair of prime factors is the prime factor itself. If there are any prime factors left unpaired, they will remain under the square root.

Step 3 ：The prime factorization of 180 gives us pairs of factors that can be taken outside the square root and the factors that remain inside the square root.

Step 4 ：The prime factorization of 180 gives us (6, 5). This means that 6 can be taken outside the square root and 5 remains inside the square root.

Step 5 ：Therefore, the simplified form of $\sqrt{180}$ is $6\sqrt{5}$

Step 6 ：Final Answer: The simplified form of $\sqrt{180}$ is $\boxed{{\displaystyle 6\sqrt{5}}}$