Question

$\ \textless \ br /\ \textgreater \ \sqrt{21.64}$
Solve with steps
​

Answer 1

ANSWER

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• Step 1:

Divide the number (21.64) by 2 to get the first guess for the square root .

First guess = 21.64/2 = 10.82.

• Step 2:

Divide 21.64 by the previous result. d = 21.64/10.82 = 2.

Average this value (d) with that of step 1: (2 + 10.82)/2 = 6.41 (new guess).

Error = new guess - previous value = 10.82 - 6.41 = 4.41.

4.41 > 0.001. As error > accuracy, we repeat this step again.

• Step 3:

Divide 21.64 by the previous result. d = 21.64/6.41 = 3.375975039.

Average this value (d) with that of step 2: (3.375975039 + 6.41)/2 = 4.8929875195 (new guess).

Error = new guess - previous value = 6.41 - 4.8929875195 = 1.5170124805.

1.5170124805 > 0.001. As error > accuracy, we repeat this step again.

• Step 4:

Divide 21.64 by the previous result. d = 21.64/4.8929875195 = 4.4226558751.

Average this value (d) with that of step 3: (4.4226558751 + 4.8929875195)/2 = 4.6578216973 (new guess).

Error = new guess - previous value = 4.8929875195 - 4.6578216973 = 0.2351658222.

0.2351658222 > 0.001. As error > accuracy, we repeat this step again.

• Step 5:

Divide 21.64 by the previous result. d = 21.64/4.6578216973 = 4.6459485584.

Average this value (d) with that of step 4: (4.6459485584 + 4.6578216973)/2 = 4.6518851279 (new guess).

Error = new guess - previous value = 4.6578216973 - 4.6518851279 = 0.0059365694.

0.0059365694 > 0.001. As error > accuracy, we repeat this step again.

• Step 6:

Divide 21.64 by the previous result. d = 21.64/4.6518851279 = 4.6518775518.

Average this value (d) with that of step 5: (4.6518775518 + 4.6518851279)/2 = 4.6518813399 (new guess).

Error = new guess - previous value = 4.6518851279 - 4.6518813399 = 0.000003788.

0.000003788 <= 0.001. As error <= accuracy, we stop the iterations and use 4.6518813399 as the square root.

So, we can say that the square root of 21.64 is 4.65188