Subtract 1119−−√−519−−√ .(1 point)
The difference is .
To subtract square roots, we subtract the numbers inside the square roots and keep the square root symbol:
√1119 - √519
Therefore, the difference is √600.
To subtract √1119 - √519, we can follow these steps:
1. Calculate the square root of 1119: √1119 ≈ 33.45
2. Calculate the square root of 519: √519 ≈ 22.81
3. Subtract the two results: 33.45 - 22.81 ≈ 10.64
Therefore, the difference is approximately 10.64.
To subtract the square roots, we can simplify each term separately and then subtract the simplified values.
Let's start by simplifying the square root of 1119.
Step 1: Prime factorize 1119:
1119 = 3 * 373
Step 2: Simplify the square root using the prime factorization:
√1119 = √(3 * 373)
= √3 * √373
Now, let's simplify the square root of 519.
Step 1: Prime factorize 519:
519 = 3 * 173
Step 2: Simplify the square root using the prime factorization:
√519 = √(3 * 173)
= √3 * √173
Now, subtract the simplified square roots:
√1119 - √519 = (√3 * √373) - (√3 * √173)
= √3(√373 - √173)
Since we cannot simplify any further, the difference of the square roots √1119 - √519 is √3(√373 - √173).