The correct answers are:
#1: A) c = √18
B) c = 3√2
C) c = 4.24
#2: A) 4/13 > 3/10
B) 79/260
#3: 4.36
Explanation:
#1: A) We use the Pythagorean Theorem to solve this:
a² + b² = c²
3² + 3² = c²
9 + 9 = c²
18 = c²
Taking the square root of each side:
√18 = √c²
√18 = c
B) To simplify √18, we first find the prime factorization of 18:
18 = 92
9 = 33
This gives us
18 = 332
When we take the square root, we are looking for pairs. We have a pair of 3's; this means we take a 3 out:
3√2
C) In the calculator, we see that 3√2 = 4.24.
#2: A) First, we find a common denominator. The first thing that both 13 and 10 will divide into is 130:
(410)/130; (313)/130
40/130; 39/130
Since 40 > 39, this means that 4/13 > 3/10.
B) There is not enough space between the two fractions to use 130 as the denominator; we will double that to 260:
(402)/260; (392)/260
80/260; 78/260
The fraction between these two would be 79/260.
#3: Using the Babylonian method, we first make a guess. Since 9 is nearly half of 19, we will start there.
Next, we divide 19 by our guess:
19/9 = 2.111
We average this quotient with our guess:
(9 + 2.111)/2 = 11.111/2 = 5.5555
This is our new guess. Now divide 19 by this guess:
19/5.5555 = 3.4200342
Average this with our guess:
(5.5555+3.4200342)/2 = 4.4877671
This is our new guess. Divide 19 by this guess:
19/4.4877671 = 4.233731291
Average this with our new guess:
(4.4877671+4.233731291)/2 = 4.360749196
This is our new guess. Divide 19 by this guess:
19/4.360749196 = 4.357049476
Average this with our new guess:
(4.360749196+4.357049476)/2 = 4.358899
Make this our new guess. Divide 19 by this guess:
19/4.358899 = 4.3588988
Average this with our guess:
(4.358899+4.3588988)/2 = 4.3588989
Since the hundredths place has been the same the last few lines, we round to that: 4.36.
