Question

√295.25 division method

I want full division method plz anybody can help me ​

Answer 1

Answer:

The following steps to find the square root by long division method

1. Draw lines over pairs of digits from right to left.

2. Find the greatest number whose square is less than or equal to the digits in the first group.

3. Take this number as the divisor and quotient of the first group and find the remainder.

4. Move the digits from the second group besides the remainder to get the new dividend.

5. Double the first divisor and bring it down as the new divisor.

6. Complete the divisor and continue the division.

7. Put the decimal point in the square root as soon as the integral part is exhausted.

8. Repeat the process till the remainder becomes zero.

Divisor

↓

Quotient

↓

3.5

3

12

.

25

9

______

6.5

3.25

3.25

______

0 ← Remainder

12.25

=3.5

Answer 2

$\large\underline{\sf{Solution-}}$

$\rm \: \sqrt{295.25}$

So, using Long Division Method, we have

$\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:17.182 \:\:}}}\\ {\underline{\sf{1}}}& {\sf{\:\:295.250000 \:\:}} \\{\sf{}}& \underline{\sf{1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }} \\ {\underline{\sf{27}}}& {\sf{195 \: \: \: \: \: \: \: \: \: \: \: }} \\{\sf{}}& \underline{\sf{189 \: \: \: \: \: \: \: \: \: \: \: }} \\ {\underline{\sf{341}}}& {\sf{\:625 \: \: \: \: }} \\{\sf{}}& \underline{\sf{\:341 \: \: \: \: }}\\ {\underline{\sf{3428}}}& {\sf{\:28400}} \\{\sf{}}& \underline{\sf{\:27424}}\\ {\underline{\sf{34361}}}& {\sf{\: \: \: \: \: \: \: \: \: 97600}} \\{\sf{}}& \underline{\sf{\: \: \: \: \: \: \: \: \: 68722}} \\ {\underline{\sf{}}}& {\sf{\:\: \: \: \: \: \: \: \: 28878}} \end{array}\end{gathered}\end{gathered}$

Hence,

$\rm\implies \:\boxed{ \bf{ \: \sqrt{295.25} = 17.182 \: \: }}$

$\rule{190pt}{2pt}$

Additional Information :-

Let evaluate $\sqrt{2}$

$\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{}}}&{\underline{\sf{\:\:1.414 \:\:}}}\\ {\underline{\sf{1}}}& {\sf{\:\:2.000000 \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: \: \: \: \: 1 \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \:\:}} \\ {\underline{\sf{24}}}& {\sf{\:\: \: \: \: \: 100 \:  \:  \:  \:   \:  \:  \:  \:\:}} \\{\sf{}}& \underline{\sf{\:\: \: \: \: 96 \:  \:  \:  \:  \:  \: \:\:}} \\ {\underline{\sf{281}}}& {\sf{\:\:400  \:\:}} \\{\sf{}}& \underline{\sf{\:\:281\:\:}} \\ {\underline{\sf{2824}}}& {\sf{\:\: \:  \: \:  \:  \:  11900\:\:}} \\{\sf{}}& \underline{\sf{\:\: \:  \:  \:  \:    \: 11296\:\:}} \\ {\underline{\sf{}}}& {\sf{\: \:  \:  \:  \:  \:  \:  \:  \:  \: \: 604\:\:}}{\sf{}}&{\sf{\:\:\:\:}}\end{array}\end{gathered}$

Hence,

$\rm\implies \:\boxed{ \bf{ \: \sqrt{2} = 1.414 \: \: }}$