Introduction:
To find the sum of 2root 5 and 3 root 7, we need to simplify the expression by combining the like terms.

Solution:
To add 2root 5 and 3 root 7, we need to first simplify each term by finding its prime factors.

Simplifying 2root 5:
2root 5 = 2 x root 5
= 2 x (5)^1/2 (since root 5 = 5^1/2)
= 2 x 5^1/2 (multiplying 2 and 5^1/2)

Simplifying 3 root 7:
3 root 7 = 3 x root 7
= 3 x (7)^1/2 (since root 7 = 7^1/2)
= 3 x 7^1/2 (multiplying 3 and 7^1/2)

Combining like terms:
Now, we have simplified both terms. Next, we need to add the two terms by combining the like terms.

2root 5 + 3 root 7 = 2 x 5^1/2 + 3 x 7^1/2 (substituting values from the simplified terms)
= 2 x 2.236 + 3 x 2.646 (finding the decimal value by using a calculator)
= 4.472 + 7.938 (multiplying and adding)
= 12.41 (adding the decimal values)

Final Answer:
Therefore, the sum of 2root 5 and 3 root 7 is 12.41.

2√5+3√7