Find the square root of 14400
The square root of 14400 is 120.
To find the square root of 14400, follow these steps:
1. Begin by estimating the square root. In this case, notice that the number 120 is close to the square root of 14400 (120 x 120 = 14400).
2. Divide 14400 by 120 to get a more accurate estimate: 14400 / 120 = 120.
3. Average the estimate and the calculated value: (120 + 120) / 2 = 120.
4. Repeat steps 2 and 3 until the estimate is accurate enough. In this case, after repeating steps 2 and 3 with the average result of 120, the estimate remains at 120.
Therefore, the square root of 14400 is 120.
To find the square root of 14400, you can use a calculator or follow these steps to manually calculate it:
1. Start by guess and check method: Take a guess at the square root of 14400. Let's start with the whole number closest to the square root of 14400, which is 120.
Calculate 120 x 120 = 14,400.
Since the guess is correct, the square root of 14400 is 120.
Alternatively, you can follow these steps using long division method:
2. Begin with the first digit of the number (1) and group the entire number into pairs starting from the decimal point.
So, 14400 becomes 14 and 400.
3. Determine the largest possible number whose square is less than or equal to 14.
In this case, it is 3 because 3 x 3 is 9.
4. Divide 14 by this number and write the quotient above the second digit of the original number.
14 ÷ 3 = 4 with a remainder of 2
Write 4 above 4 in 14400.
5. Repeat the process by bringing down the next pair (400).
6. Double the quotient (4 in this case) and write it on the right of the current number. This will become the new divisor.
Double of 4 is 8.
7. Find a number to fill in the blank of "__×__=___". This number, when placed in the blank, should make the product less than or equal to the current dividend. Write this number above the rightmost digit of the current number.
In this case, 8 x 8 = 64.
Write 8 above 400.
8. Multiply the entire divisor (48) by the new digit (8) and subtract it from the current number.
400 - 384 = 16
9. Bring down the next pair, in this case, 00.
10. Double the quotient from step 8 (48) and repeat steps 7 and 8 until you have brought down all the pairs.
Double of 48 is 96.
Multiply 96 by a number (in this case, 2) to get 192.
Subtract 192 from 1600 (which is 1600 - 192) to get 1408.
Bring down the next pair (00).
11. Repeat steps 7 and 8 until all pairs are used.
Double of 489 is 978.
Multiply 978 by a number (in this case, 2) to get 1956.
Subtract 1956 from 1408 to get -548.
As there are no more pairs to bring down, you have completed the division.
12. The whole number part of the quotient is the approximate square root of 14400.
In this case, it is 120.
Therefore, the approximate square root of 14400 is 120.