Question

find square root of 37.22 correct upto two places of decimal​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Here is the answer to questions like: What is the square root of 37.22? | √37.22 or what is the square root of 37.22?

Use the square root calculator below to find the square root of any imaginary or real number. See also in this web page a Square Root Table from 1 to 100 as well as the Babylonian Method or Hero's Method.

The Babylonian Method also known as Hero's Method

See below how to calculate the square root of 37.22 step-by-step using the Babylonian Method also known as Hero's Method.

In this case we are going to use the 'Babylonian Method' to get the square root of any positive number.

We must set an error for the final result. Say, smaller than 0.001. In other words we will try to find the square root value with at least 2 correct decimal places.

Step 1:

Divide the number (37.22) by 2 to get the first guess for the square root .

First guess = 37.22/2 = 18.61.

Step 2:

Divide 37.22 by the previous result. d = 37.22/18.61 = 2.

Average this value (d) with that of step 1: (2 + 18.61)/2 = 10.305 (new guess).

Error = new guess - previous value = 18.61 - 10.305 = 8.305.

8.305 > 0.001. As error > accuracy, we repeat this step again.

Step 3:

Divide 37.22 by the previous result. d = 37.22/10.305 = 3.6118389131.

Average this value (d) with that of step 2: (3.6118389131 + 10.305)/2 = 6.9584194566 (new guess).

Error = new guess - previous value = 10.305 - 6.9584194566 = 3.3465805434.

3.3465805434 > 0.001. As error > accuracy, we repeat this step again.

Step 4:

Divide 37.22 by the previous result. d = 37.22/6.9584194566 = 5.3489158324.

Average this value (d) with that of step 3: (5.3489158324 + 6.9584194566)/2 = 6.1536676445 (new guess).

Error = new guess - previous value = 6.9584194566 - 6.1536676445 = 0.8047518121.

0.8047518121 > 0.001. As error > accuracy, we repeat this step again.

Step 5:

Divide 37.22 by the previous result. d = 37.22/6.1536676445 = 6.0484254513.

Average this value (d) with that of step 4: (6.0484254513 + 6.1536676445)/2 = 6.1010465479 (new guess).

Error = new guess - previous value = 6.1536676445 - 6.1010465479 = 0.0526210966.

0.0526210966 > 0.001. As error > accuracy, we repeat this step again.

Step 6:

Divide 37.22 by the previous result. d = 37.22/6.1010465479 = 6.1005926947.

Average this value (d) with that of step 5: (6.1005926947 + 6.1010465479)/2 = 6.1008196213 (new guess).

Error = new guess - previous value = 6.1010465479 - 6.1008196213 = 0.0002269266.

0.0002269266 <= 0.001. As error <= accuracy, we stop the iterations and use 6.1008196213 as the square root.

So, we can say that the square root of 37.22 is 6.1

Step-by-step explanation:

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