sqrt of 450 simplified with solution
Simplify the radical by breaking the radicand up into a product of known factors.
Exact Form:
15
√
2
15
2
Decimal Form:
21.21320343
To simplify the square root of 450, we can first factorize the number 450. Let's start by finding the prime factors:
450 ÷ 2 = 225
225 ÷ 3 = 75
75 ÷ 3 = 25
25 ÷ 5 = 5
The prime factorization of 450 is 2 * 3 * 3 * 5 * 5.
Next, we can group the prime factors in pairs and take out each pair of the same factors from the square root:
sqrt(450) = sqrt(2 * 3 * 3 * 5 * 5)
= sqrt(2 * 3 * 3) * sqrt(5 * 5)
= 3 * sqrt(2) * 5
= 15 * sqrt(2)
So, the simplified form of the square root of 450 is 15 * sqrt(2).