simplify: sqrt (90)
a) 30
b) 3 sqrt (10)
c) 10 srt (3)
d) 9 sqrt (3)
sqrt (9*2*5)
3 sqrt (10)
thanks
To simplify the square root of 90, you need to find perfect squares that divide evenly into 90.
Here's how you can do it:
1. Break down 90 into its prime factors: 90 = 2 * 3 * 3 * 5.
2. Rewrite the square root of 90 as the product of the square root of the perfect squares within the prime factorization.
- sqrt(90) = sqrt(2 * 3 * 3 * 5)
3. Identify the perfect squares:
- 2 * 3 * 3 can be simplified as 3 * 3 = 9.
- The remaining prime factor 5 does not have a matching factor.
- So, we can rewrite sqrt(90) as sqrt(9 * 5).
4. Simplify:
- sqrt(9 * 5) = sqrt(9) * sqrt(5) = 3 * sqrt(5).
Therefore, the simplified form of sqrt(90) is option d) 9 sqrt(3).