Question

Find the square root of 10 correct to four places of decimal

Answer 1

guess and divide method.
Step–1: Estimate perfect square root as close as possible to your number.Step–2: Divide your number by that square root.Step–3: Calculate the average of the result of step 2 and the root.Step–4: Use the result of step 3 to repeat steps 2 and 3 until you have a number that is accurate enough for you.
Calculate the square root of 10 (√ 10) to 4 decimal places.
1.    Find the perfect square number closer to 10. 32 = 9 and 42 = 16, so take 3.2.    Divide 10 by 3. 10÷3 = 3.33 (you can round off the answer)3.    Average 3.33 and 3. (3.33 + 3)÷2 = 3.1667
Repeat step 2: 10÷3.1667 = 3.1579Repeat step 3: Average 3.1579 and 3.1667.(3.1579 + 3.1667)÷2 = 3.1623

Answer 2

Answer:

$\sqrt{10}=3.1622$            

Step-by-step explanation:

Given : Number $\sqrt{10}$

To find : The square root of 10 correct to four places of decimal?

Solution :

To find the square root of a non perfect square natural number :

1. Group the digits into pairs

2. Find the largest number whose square is less than or equal to the number then divide and get the remainder.

3. Put a decimal point and place zero and pairing into two.

4. Divide again and write remainder till it comes to zero.

5. Follow this process up to four decimal places.

Now, The division method by square root calculator is shown below in the figure.

Refer the attached graph below.

$\sqrt{10}=3.1622$ up to four decimal places.