Find the square root of 169: √169 .(1 point)
Responses
−13
negative 13
13,−13
13 comma negative 13
84.5
84.5
13
13
are you sure?
Apologies for the confusion. The square root of 169 is:
13
To find the square root of 169, there are a couple of methods you can use. One method is to use a calculator with a square root function. Simply enter 169 into the calculator and press the square root button (√) to get the result.
Another method is to manually calculate the square root using long division. Here's how you can do it:
1. Start by making pairs of digits from the rightmost side of the number. In this case, we can pair the digits as 16 and 9.
2. Find the largest integer whose square is less than or equal to the first pair of digits. In this case, the largest integer whose square is less than or equal to 16 is 4.
3. Write the square root of that integer (4) as the divisor on the left, and write the pair of digits (16) as the dividend on the right.
4. Divide the leftmost pair of digits by the divisor and write the quotient on top. In this case, 16 divided by 4 is 4, so we write 4 on top.
5. Multiply the divisor by the quotient and write the result under the dividend. In this case, 4 multiplied by 4 is 16.
6. Subtract the result from the dividend. In this case, 16 minus 16 is 0.
7. Bring down the next pair of digits (9) to the right of the difference.
8. Double the divisor and write the result on the left next to the previous quotient. In this case, 4 doubled is 8, so we write 48 on top.
9. Find the largest digit x to fill in the blank in 4x(x + 1) such that 4x(x + 1) * x does not exceed 90 (the current dividend).
- In this case, the largest digit x for which 4x(x + 1) * x does not exceed 90 is 3. So, we write 3 as the next digit of the quotient.
10. Multiply the entire product 4(40 + 3) by 3. 4(40 + 3) * 3 = 432.
11. Place the result (432) below the dividend (90) and subtract.
12. The result is 42.
13. Repeat steps 7 to 12 until you have a remainder of 0 or until you have obtained the desired level of precision.
In this case, the square root of 169 is 13.