Simplify 799−−√ .
The square root of 799 cannot be simplified further. Thus, the simplified form is √799.
To simplify the expression 799−−√, we need to find the square root of 799.
Step 1: Prime Factorization of 799
To find the prime factorization of 799, we can start dividing it by prime numbers.
799 ÷ 2 = 399.5 (not a whole number)
799 ÷ 3 = 266.333 (not a whole number)
799 ÷ 5 = 159.8 (not a whole number)
799 ÷ 7 = 114.14 (not a whole number)
799 ÷ 11 = 72.636 (not a whole number)
799 ÷ 13 = 61.462 (not a whole number)
799 ÷ 17 = 47 (whole number)
Therefore, the prime factorization of 799 is 17 × 47.
Step 2: Simplifying the Square Root
The square root of a number can be simplified by grouping the factors into pairs.
√(17×47) = √(17) × √(47)
So, the simplified expression of 799−−√ is √(17) × √(47).
To simplify the expression 799-√, we need to find the square root of 799 and subtract it.
To find the square root, you can use a calculator or manually approximate it. Let's use a calculator to find the square root of 799.
√799 ≈ 28.240
Now we can subtract this value from 799:
799 - 28.240 ≈ 770.760
So, simplify 799-√ is approximately equal to 770.760.