simplify the radical expression of sqrt486
explain your work
To simplify the radical expression √486, we need to find perfect square factors of 486.
First, we can note that 486 is divisible by 2:
486 ÷ 2 = 243
243 cannot be further simplified, so we can write:
√486 = √(2 * 243)
Next, let's consider the number 243. It is divisible by 3:
243 ÷ 3 = 81
81 can be simplified further since it's a perfect square:
√81 = 9
Therefore:
√486 = √(2 * 81) = √(2 * 9 * 9) = √(2 * 3²) = 3√2
Final Simplification:
√486 = 3√2
To simplify the radical expression √486, we need to find the factors of 486 and look for any perfect square factors.
The prime factorization of 486 is 2 × 3^5.
Now, let's group the factors in pairs of equal values:
√(2 × 3 × 3 × 3 × 3 × 3)
Since we have two sets of 3^2, we can take them out from under the square root:
3 × 3 × √(2)
Simplifying further:
9√2
So, the simplified form of √486 is 9√2.