Express 44100 as a product of its least prime factors
Let's distribute the coefficients to simplify the expression:
4(2n+3m)+5(n+2m) = 8n + 12m + 5n + 10m
= (8n + 5n) + (12m + 10m)
= 13n + 22m
Therefore, the simplified expression is 13n + 22m.
We can start by finding the smallest prime factor of 44100:
44100 = 2 x 22050
Now we need to find the smallest prime factor of 22050:
22050 = 2 x 11025
The next step is to find the smallest prime factor of 11025:
11025 = 3 x 3675
Lastly, we need to find the smallest prime factor of 3675:
3675 = 3 x 1225
Since 1225 is the square of a prime number, we can stop here. Therefore:
44100 = 2 x 3 x 3 x 5 x 7 x 5 x 7 = 2^2 x 3^2 x 5^2 x 7^2
Find the square root of 36/25
We can simplify 36/25 as (6/5)^2. Therefore, the square root of 36/25 is equal to the absolute value of 6/5, which is 6/5 or 1.2.
Find the square root of 3/6/25
We can simplify 3/6/25 as follows:
3/6/25 = 3 ÷ (6/25) = 3 × (25/6) = 15/2
Therefore, we need to find the square root of 15/2. To simplify this expression, we can write:
15/2 = (3 × 5)/(1 × 2) = 3 × 5/2
Taking the square root of both sides gives:
sqrt(15/2) = sqrt(3 × 5/2) = sqrt(3) × sqrt(5/2) = sqrt(3) × sqrt(5) ÷ sqrt(2)
We can rationalize the denominator by multiplying both the numerator and denominator by sqrt(2):
sqrt(3) × sqrt(5) ÷ sqrt(2) = sqrt(3) × sqrt(5) / sqrt(2) × sqrt(2)
= sqrt(15) / 2
Therefore, the square root of 3/6/25 is equal to sqrt(15) / 2.
Simplify the Expression 4(2n+3m)+5(n+2m)
Simplify the Expression 2(c+12)+4(c-3
Let's distribute the coefficients to simplify the expression:
2(c+12)+4(c-3) = 2c + 24 + 4c - 12
= 6c + 12
We can then factor out a 6 from both terms:
6c + 12 = 6(c + 2)
Therefore, the simplified expression is 6(c + 2).