Simplify by factoring.
radical 90
sqrt (9*10) = sqrt (3*3*10) = 3 sqrt (10)
take factors, beginning with the least common factors.
ex: 90=3,3,10
two 3s (three squared) mean you take a three out, multiplying it by the square root of ten left.
To simplify the expression radical 90, we begin by finding the factors of 90.
The prime factorization of 90 can be found by dividing it successively by prime numbers:
90 ÷ 2 = 45
45 ÷ 3 = 15
15 ÷ 3 = 5
So, the prime factorization of 90 is 2 × 3 × 3 × 5.
Now, let's rearrange the factors in ascending order:
90 = 2 × 3 × 3 × 5
Next, we can group the factors into pairs of identical factors and take their square roots:
90 = √(2 × 3 × 3 × 5)
= √(2 × 3 × 3) × √5
= 3√2 × √5
Therefore, the simplified form of radical 90 is 3√2 × √5.