Express in simplest radical form
√162
To express √162 in simplest radical form, we can first factor 162.
162 can be factored as 2 * 3^4.
Taking the square root of 2 * 3^4, we can separate the factors.
√(2 * 3^4) = √(2) * √(3^4)
Taking the square root of 3^4, we can simplify further.
√(2) * √(3^4) = √(2) * 3^2
Therefore, √162 in simplest radical form is 3√2.
To express √162 in simplest radical form, we need to find the largest perfect square that is a factor of 162.
The prime factorization of 162 is:
162 = 2 × 3 × 3 × 3 × 3
Now, let's group the factors of 162 in pairs of twos:
162 = (2 × 3) × (3 × 3 × 3)
By simplifying the pairs of twos, we get:
162 = 6 × 9
Now, let's express 9 as a perfect square:
162 = 6 × (3 × 3)
Simplifying further, we get:
162 = 6 × 3²
Finally, we can take the square root of 3²:
√162 = √(6 × 3²)
√162 = √6 × √(3²)
√162 = √6 × 3
Therefore, the simplest radical form of √162 is 3√6.
Not right bot
Apologies for the error. Let's factor 162 to find the largest perfect square factor.
The prime factorization of 162 is:
162 = 2 × 3 × 3 × 3 × 3
Now, let's group the factors of 162 in pairs:
162 = (2 × 3) × (3 × 3 × 3)
Simplifying the pairs, we have:
162 = 6 × 27
However, 27 is not a perfect square. We can continue factoring it:
27 = 3 × 9
Now, let's express 9 as a perfect square:
27 = 3 × (3 × 3)
Simplifying further, we get:
27 = 3 × 3²
Now, we can substitute this back into the factorization of 162:
162 = 6 × (3 × 3²)
162 = 6 × 3 × 3²
Finally, we can simplify the square root of 3²:
√162 = √(6 × 3 × 3²)
√162 = √6 × √(3 × 3²)
√162 = √6 × 3
Therefore, the simplest radical form of √162 is 3√6.
To express √162 in simplest radical form, we need to find the factors of 162 and simplify as much as possible.
First, we can find the prime factorization of 162:
162 ÷ 2 = 81
81 ÷ 3 = 27
27 ÷ 3 = 9
9 ÷ 3 = 3
So, the prime factorization of 162 is 2^1 × 3^4.
Now, we can rewrite√162 using the prime factorization:
√162 = √(2^1 × 3^4)
Using the property of radicals, we can separate the radicals for each factor:
√162 = √(2^1) × √(3^4)
Taking the square root of each factor:
√162 = √2 × √(3^2 × 3^2)
Simplifying the square roots:
√162 = √2 × (3 × 3)
Multiplying the simplified factors:
√162 = 3√2
So, the simplest radical form of √162 is 3√2.