Answer:
The square root of 841 by division method is 29
Step-by-step explanation:
We are given a whole number and are asked to find out the square root of the number by the long division method.
We will be solving the given question stepwise using the rules to find the square root by the long division method.
According to our question, we need to find the square root of 841 using the division method.
Firstly, we group the digits in pairs starting from the unit’s place. Each pair is referred to as a period.
Following the same, the number 841 can be grouped into two periods.
⇒1stperiod=08
⇒2ndperiod=41
)08 41¯¯¯¯¯¯¯¯¯¯¯¯¯
Next, we take the number as quotient and divisor whose square of the number is less than or equal to 1st period.
In our case,
⇒1stperiod=08
We know that the value of 22=4
From the above, we can say that the square of the number 2 is less than 8.
Following the same, we get,
⇒divisor=2
⇒quotient=2
We need to place the numbers 2 and 4 in the long division as follows,
2)084104¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯2
Subtracting the product of divisor and quotient from the 1st period, we get,
⇒remainder=8−(2×2)
Simplifying the above equation, we get,
⇒remainder=8−4
⇒remainder=4
The remainder through long division is shown as follows,
2⎞⎠⎟084104−−−−−4¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯2
Appending the 2nd period to the remainder, we get,
⇒new dividend=441
Showing the same through long division, we get,
2⎞⎠⎟084104−−−−−441¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯2
Now, we need to square the quotient
⇒22=4
We need to find a number such that
⇒4_×_≤441
By the trial-and-error method, we find that the largest number satisfying the inequality is 9.
Substituting the value of 9 in the inequality, we get,
⇒49×9=441
We need to place the numbers 9 and 441 in the long division as follows,
2)8414¯¯¯¯¯¯¯¯¯¯¯¯¯2949)441441¯¯¯¯¯¯¯¯¯¯¯¯¯
Subtracting the number 441 from the new dividend, we get,
The long division is represented as follows,
2)8414¯¯¯¯¯¯¯¯¯¯¯¯¯2949⎞⎠⎟441441−−−0¯¯¯¯¯¯¯¯¯¯¯¯¯
The value of the remainder is zero. Hence, the long division has been performed.
therefore 841 square root is 9
*******************************plz mark me brainliest**********************
