To simplify the expression 93−72, we need to first simplify the square root in the numerator. The square root of 72 can be broken down into its prime factors, and then simplified. After simplifying the square root, we can simplify the entire fraction by dividing both the numerator and the denominator by their greatest common divisor.
Step 1: Simplify the Square Root
First, we need to simplify the square root in the expression 72. We can do this by finding the prime factorization of 72:
72=23×32
Using the property of square roots, a×b=a×b, we can simplify:
72=23×32=22×2×32=22×32×2=2×3×2=62
Step 2: Substitute the Simplified Square Root
Substitute 72=62 back into the original expression:
93−72=93−62
Step 3: Simplify the Fraction
Now, simplify the fraction by dividing each term in the numerator by the denominator: