Question

HIIII❤❤❤❤❤$find \: the \: value \: of \: \sqrt{5} correctto \: two \: decimal \: places$
Then find the value of the square root of
$3 - \sqrt{5} \div 3 + \sqrt{5}$
correct to two decimal places.

NEED QUICK ANSWER!!!!
​

Answer 1

Solution :

We've to find the value of √5 correct to two decimal places. In order to find the approximate square roots of numbers decimals up to certain decimals Long Division Method is used.

Step to find the square root by long division method :

Step 1 : Mark off the digits in pairs starting with the ones digit.

Step 2 : Think of the largest number whose square is either equal to or just less than the first period from left. Put the quotient above the period and write the product of divisor and quotient just below the first period.

Step 3 : Find the remainder

Step 4 : Bring down the next pair of digits to the right of the remainder. This is the new dividend

Step 5 : Double the current quotient and enter it as a divisor with a blank on its right.

Step 6 : Guess the largest possible digit to fill the blank as the new quotient such that when it is multiplied the new divisor,the product is either less or equal to the dividend.

Step 7 : Now, subtract the product of new divisor and the new digit from the new dividend.

Step 8 : If reminder is zero and no period is left,then we stop and current quotient is square root of given number. If remainder is non-zero,then repeat the Steps from 5 to 8 till all the periods have been taken care of. ________________________________

[ Refer to the attachment. ]

Now It is clear that √5 = 2.236

We are required to find sqaure root of 5 Correct to two decimal places. Here,we've found the square root of upto 4 decimal places. In the third place, we've 6 >5 and therefore,1 is added to the second decimal place [

$\therefore$ √5 = 2.24

Let's move further :

We've to find the value of :

$\longrightarrow \sf \: 3 - \sqrt{5} \div 3 + \sqrt{5}$

Put the value of √5 = 2.24

$\longrightarrow \sf \: 3 - 2.24 \div 3 + 2.24$

$\longrightarrow \sf \: 3 - 0.7466+ 2.24$$\longrightarrow \sf \: 5.24 - 0.7466$$\longrightarrow \sf \: 4.4934 \: (Approx)$

Correct to two decimal places :$\longrightarrow \sf \: Required \: Value = \large \boxed{ \purple{ \sf 4.49}}$

Answer 2

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.

Hence,

√5 = 2.23 (correct upto two decimal place)

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