Question

423.74 find the square root of decimal numbers correct to 2 places of decimals

Answer 1

Steps to be followed to find the square root of 423.74 correct to 2 places of decimals are as follows and the square root of 423.74 is 20.58

• Step 1:
• Divide the number (423.74) by 2 to get the first guess for the square root.
• Guess = 423.74/2 = 211.87.

• Step 2:
• Divide 423.74 by the previous result. d = 423.74/211.87 = 2.
• Average this value (d) with that of step 1: (2 + 211.87)/2 = 106.935  

• Step 3:
• Divide 423.74 by the previous result. d = 423.74/106.935 = 3.9625940992.
• Average this value (d) with that of step 2: (3.9625940992 + 106.935)/2 = 55.4487970496  

• Step 4:
• Divide 423.74 by the previous result. d = 423.74/55.4487970496 = 7.6420052832.
• Average this value (d) with that of step 3: (7.6420052832 + 55.4487970496)/2 = 31.5454011664  

• Step 5:
• Divide 423.74 by the previous result. d = 423.74/31.5454011664 = 13.4327028452.
• Average this value (d) with that of step 4: (13.4327028452 + 31.5454011664)/2 = 22.4890520058  

• Step 6:
• Divide 423.74 by the previous result. d = 423.74/22.4890520058 = 18.8420570103.
• Average this value (d) with that of step 5: (18.8420570103 + 22.4890520058)/2 = 20.6655545081

• Step 7:
• Divide 423.74 by the previous result. d = 423.74/20.6655545081 = 20.504651827.
• Average this value (d) with that of step 6: (20.504651827 + 20.6655545081)/2 = 20.5851031676  

• Step 8:
• Divide 423.74 by the previous result. d = 423.74/20.5851031676 = 20.584788745.
• Average this value (d) with that of step 7: (20.584788745 + 20.5851031676)/2 = 20.5849459563

• Therefore, we can say that the square root of 423.74 is 20.58

Answer 2

Step-by-step explanation:

Given that:423.74 find the square root of decimal numbers correct to 2 places of decimals

To find: Square root

Solution:

Make pair of two digits from left to right after decimal and right to left before decimal point

2)423.74(20.584

4

______

405)2374

2025

_________

4108 ) 34900

32864

__________

41164 )203600

164656

_________

38944

Thus,

$\sqrt{423.74} = 20.584$

Hope it helps you.