find the value of √2345√2345√2345√2345√2345√2345√2345√2345
Answers
Answer:
Step 1)
Set up 2345 in pairs of two digits from right to left and attach one set of 00 because we want one decimal:
23 45 00
Step 2)
Starting with the first set: the largest perfect square less than or equal to 23 is 16, and the square root of 16 is 4. Therefore, put 4 on top and 16 at the bottom like this:
4
23 45 00
16
Step 3)
Calculate 23 minus 16 and put the difference below. Then move down the next set of numbers.
4
23 45 00
16
7 45
Step 4)
Double the number in green on top: 4 × 2 = 8. Then, use 8 and the bottom number to make this problem:
8? × ? ≤ 745
The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 8. Replace the question marks in the problem with 8 to get:
88 × 8 = 704.
Now, enter 8 on top, and 704 at the bottom:
4 8
23 45 00
16
7 45
7 04
Step 5)
Calculate 745 minus 704 and put the difference below. Then move down the next set of numbers.
4 8
23 45 00
16
7 45
7 04
0 41 00
Step 6)
Double the number in green on top: 48 × 2 = 96. Then, use 96 and the bottom number to make this problem:
96? × ? ≤ 4100
The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 4. Now, enter 4 on top:
4 8 4
23 45 00
16
7 45
7 04
0 41 00
That's it! The answer is on top. The square root of 2345 with one digit decimal accuracy is 48.4. Did you notice that the last two steps repeat the previous two steps. You can add decimals by simply adding more sets of 00 and repeating the last two steps over and over.