Question

Evaluate the following:
a) 6.24
$\times$
4.2?
write in the correct digit
​

Answer 1

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Answer:

Dear , your answer is here :

The square root of 6.24 is 2.4979991993594. Or,

√6.24 = 2.4979991993594

Step-by-step explanation:

Step 1:

Divide the number (6.24) by 2 to get the first guess for the square root .

First guess = 6.24/2 = 3.12.

Step 2:

Divide 6.24 by the previous result. d = 6.24/3.12 = 2.

Average this value (d) with that of step 1: (2 + 3.12)/2 = 2.56 (new guess).

Error = new guess - previous value = 3.12 - 2.56 = 0.56.

0.56 > 0.001. As error > accuracy, we repeat this step again.

Step 3:

Divide 6.24 by the previous result. d = 6.24/2.56 = 2.4375.

Average this value (d) with that of step 2: (2.4375 + 2.56)/2 = 2.49875 (new guess).

Error = new guess - previous value = 2.56 - 2.49875 = 0.06125.

0.06125 > 0.001. As error > accuracy, we repeat this step again.

Step 4:

Divide 6.24 by the previous result. d = 6.24/2.49875 = 2.4972486243.

Average this value (d) with that of step 3: (2.4972486243 + 2.49875)/2 = 2.4979993122 (new guess).

Error = new guess - previous value = 2.49875 - 2.4979993122 = 0.0007506878.

0.0007506878 <= 0.001. As error <= accuracy, we stop the iterations and use 2.4979993122 as the square root.

So, we can say that the square root of 6.24 is 2.497 with an error smaller than 0.001 (in fact the error is 0.0007506878). this means that the first 3 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(6.24)' is 2.4979991993593593.

Note: There are other ways to calculate square roots. This is only one of them.

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