What does 12 (plus/minus symbol) sqrt142 equal?
12 ± √142 is just that!
This is called an "exact" answer
If you want a decimal approximation, pull out your calculator.
Oh, okay! Thanks, Reiny!
To evaluate the expression "12 ± √142", we first need to find the values of both the positive and negative square roots of 142. Here's how you can do it:
Step 1: Start with the number 142.
Step 2: Find the prime factors of 142. In this case, 142 is a composite number. It can be written as 2 × 71.
Step 3: Take the square root of each prime factor. The square root of 2 is approximately 1.414, and the square root of 71 is approximately 8.426.
Step 4: Combine the square roots with their respective signs: +√2 and -√2, as well as +√71 and -√71.
Now, substituting the square roots into the original expression:
12 ± √142 = 12 ± (√2 × √71)
So the resulting expressions are:
12 + √142 = 12 + (√2 × √71) ≈ 12 + (1.414 × 8.426)
12 - √142 = 12 - (√2 × √71) ≈ 12 - (1.414 × 8.426)
After performing the calculations, the two expressions will yield the numerical values for positive and negative square roots of 142 respectively.