Question

divide.
$sqrt5{36.65}$

Explanation:

Step1: Divide 36 by 5

5 goes into 36 seven times (5×7 = 35). Subtract 35 from 36: 36 - 35 = 1. Bring down the 6 to make 16.

Step2: Divide 16 by 5

5 goes into 16 three times (5×3 = 15). Subtract 15 from 16: 16 - 15 = 1. Bring down the 6 to make 16 (wait, no, the number is 36.65, so after 36 ÷ 5 = 7 with remainder 1, we bring down the 6 (the tenths place) to get 16 tenths. Wait, maybe better to do decimal division properly.

Let's rewrite 36.65 ÷ 5.

We can think of 36.65 as 36 + 0.6 + 0.05.

Divide each part by 5:

36 ÷ 5 = 7.2? Wait no, 5×7 = 35, remainder 1. Then 1 (which is 1.0) + 0.6 = 1.6. 1.6 ÷ 5 = 0.32. Then 0.05 ÷ 5 = 0.01. Wait, no, let's do long division:

    7.33
  _______
5 | 36.65
    35
    ---
     1 6
     1 5
     ---
      1 5
      1 5
      ---
       0

Wait, 5×7 = 35, subtract from 36, get 1. Bring down the 6 (from 36.65) to make 16. 5×3 = 15, subtract from 16, get 1. Bring down the 5 (from the hundredths place) to make 15. 5×3 = 15, subtract, get 0. So 36.65 ÷ 5 = 7.33? Wait no, 5×7.33 = 36.65? Let's check: 5×7 = 35, 5×0.3 = 1.5, 5×0.03 = 0.15. So 35 + 1.5 + 0.15 = 36.65. Yes! So 36.65 ÷ 5 = 7.33? Wait no, 5×7.33 is 36.65? Wait 7.33×5: 7×5=35, 0.3×5=1.5, 0.03×5=0.15. 35+1.5=36.5, +0.15=36.65. Yes. Wait, but let's do the long division correctly:

    7.33
  _______
5 | 36.65
    35
    ---
     1 6   (bring down the 6, making 16 tenths)
     1 5   (5×3=15, subtract)
     ---
      1 5   (bring down the 5, making 15 hundredths)
      1 5   (5×3=15, subtract)
      ---
       0

Wait, so 36.65 ÷ 5 = 7.33? Wait no, wait 36.65 divided by 5:

36 ÷ 5 = 7, remainder 1. Then 1 (which is 1.0) + 0.6 = 1.6. 1.6 ÷ 5 = 0.32. Then 0.05 ÷ 5 = 0.01. Wait, 7 + 0.32 + 0.01 = 7.33. Yes, that's correct.

Wait, maybe I made a mistake earlier. Let's do it step by step:

1. 5 into 36 (the whole number part) is 7, because 5×7=35. Subtract 35 from 36: 36-35=1.
2. Bring down the 6 (the tenths place) to make 16 tenths (1.6).
3. 5 into 1.6 is 0.3, because 5×0.3=1.5. Subtract 1.5 from 1.6: 1.6-1.5=0.1.
4. Bring down the 5 (the hundredths place) to make 1.5 (wait, no, 0.1 is 1 tenth, bring down 5 hundredths to make 10 hundredths + 5 hundredths = 15 hundredths (0.15).
5. 5 into 0.15 is 0.03, because 5×0.03=0.15. Subtract 0.15 from 0.15: 0.15-0.15=0.

Now, add up the parts: 7 (from the whole number) + 0.3 (from tenths) + 0.03 (from hundredths) = 7.33.

Wait, but let's check 7.33×5: 7×5=35, 0.3×5=1.5, 0.03×5=0.15. 35+1.5=36.5, 36.5+0.15=36.65. Perfect, that's the original number. So the quotient is 7.33.

Wait, but maybe I messed up the long division steps. Let's do long division properly:

    7.33
  _______
5 | 36.65
    35
    ---
     1 6   (after 36-35=1, bring down 6: 16 tenths)
     1 5
     ---
      1 5   (bring down 5: 15 hundredths)
      1 5
      ---
       0

Yes, that's correct. So each step:

• 5×7=35, subtract from 36: remainder 1.
• Bring down 6 (from 36.65) to make 16 (tenths place, so 1.6).
• 5×3=15, subtract from 1.6: remainder 0.1.
• Bring down 5 (hundredths place) to make 1.5 (hundredths? Wait, no, 0.1 is 10 hundredths, plus 5 hundredths is 15 hundredths, which is 0.15).
• 5×3=15, subtract from 0.15: remainder 0.

So the decimal places: 7 (ones), 3 (tenths), 3 (hundredths). So 7.33.

Answer:

7.33