Find the square root of 169: √169
A. 13, - 13
B: 13
C. -13
D. 84.5
The square root of 169 is 13, so the correct answer is B. 13
To find the square root of a number, you can use a calculator, or you can use a manual method. Let's use the manual method to find the square root of 169.
Step 1: Take any number that when squared, gives a result less than or equal to 169. In this case, we can start with the number 13.
Step 2: Square the number obtained in Step 1. 13 squared is 169.
Step 3: Compare the result obtained in Step 2 to the original number. If the numbers are the same, then the square root is the number used in Step 1. In this case, 169 is equal to 169, so the square root is 13.
Thus, the correct answer is B. 13.
To find the square root of 169, you can either calculate it manually or use a calculator.
If you calculate it manually, you can use the following method:
1. Start with any guess for the square root. Let's start with 13.
2. Divide 169 by 13: 169 / 13 = 13
3. Take the average of the previous guess and the result of the division: (13 + 13) / 2 = 13
4. Repeat steps 2 and 3 until the square root is found:
- Divide 169 by 13: 169 / 13 = 13
- Take the average of 13 and 13: (13 + 13) / 2 = 13
- Repeat the division and the average until the number stops changing:
- Divide 169 by 13: 169 / 13 = 13
- Take the average of 13 and 13: (13 + 13) / 2 = 13
- The square root of 169 is 13.
Therefore, the correct answer is B: 13.
find the cube root of -729: ∛-729
A. 9, -9
B. -9
C. 9
D.243
To find the cube root of -729, you can use the following steps:
Step 1: Determine the sign of the cube root by looking at the given number. In this case, since -729 is a negative number, the cube root will be negative.
Step 2: Take the absolute value of the number to find the cube root of the magnitude. In this case, the absolute value of -729 is 729.
Step 3: Find the cube root of the absolute value. The cube root of 729 is 9.
Step 4: Apply the sign determined in Step 1 to the result from Step 3. Since the sign is negative, the cube root of -729 is -9.
Therefore, the correct answer is A. 9, -9.
find the cube root of -8: ∛-8
To find the cube root of -8, you can use the following steps:
Step 1: Determine the sign of the cube root by looking at the given number. In this case, since -8 is a negative number, the cube root will be negative.
Step 2: Take the absolute value of the number to find the cube root of the magnitude. In this case, the absolute value of -8 is 8.
Step 3: Find the cube root of the absolute value. The cube root of 8 is 2.
Step 4: Apply the sign determined in Step 1 to the result from Step 3. Since the sign is negative, the cube root of -8 is -2.
Therefore, the correct answer is: ∛-8 = -2.
Find the cubic root of 135
A. 3 ∛5
B. 3√5
C. 5∛27
D. ∛5
To find the cubic root of 135, we need to find a number that, when raised to the power of 3, gives us 135.
We can start by trying different values. Let's start with 3:
3^3 = 27
4^3 = 64
5^3 = 125
6^3 = 216
Since 5^3 is closest to 135, the cubic root of 135 is 5.
Therefore, the correct answer is C. 5∛27.
What is the circumference of a circle with a diameter of 4.5 miles estimate the circumference to the hundredths place using 3.14 for pie
A. 7.07 miles
B. 14.2 miles
C. 63.59 miles
D 14.13 miles