when the square root of 450 is simplified, the coefficient of the mixed radical is?

sqrt(450) = sqrt(2*225) = 15*sqrt(2).

sqrt of 450 simplified solution

To simplify the square root of 450 and find the coefficient of the mixed radical, we need to factorize 450 into its prime factors.

The prime factorization of 450 can be found by dividing it by prime numbers starting from 2 until the quotient becomes 1:

450 ÷ 2 = 225
225 ÷ 3 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5

The prime factorization of 450 is 2^1 × 3^2 × 5^2.

Now, let's simplify the square root of 450 using the concept that the square root of a product is equal to the product of the square roots of its factors:

√450 = √(2^1 × 3^2 × 5^2)
= √(2^1) × √(3^2) × √(5^2)
= √2 × 3 × 5

Since the square root of 2 is irrational, we cannot simplify it any further, so the coefficient of the mixed radical is 3 × 5 = 15.

Therefore, the coefficient of the mixed radical in the simplified form of √450 is 15.