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find the value of under root 5 ? briefly.?

To find the value we have to do long division method.

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i htink 2.24

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For this, we draw a number line and mark the integers −2, −1, 0, 1, 2, 3, 4, etc. on it, so that the distance between any two consecutive integers is one unit. On this number line, we mark O and A at the points 0 and 2 respectively. At A, we draw AB of unit length which is perpendicular to OA. Now, we join OB. Taking O as the centre and OB as the radius, we will draw an arc which cuts the number line at P.

Now, point P represents the irrational numberon the number line. Let us verify it.

Using Pythagoras theorem in ΔOAB,

OB2 = OA2 + AB2

= 22 + 12

= 4 + 1

= 5

But OP = OB

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Square root of 5 is found in long division method to find square root of 5 up to desire number of decimal placesp, we put 2(p + 1) number of zero after the decimal place. Then we find the square root of this number up to p+ 1 places of decimal. Then we round up the values up to p places of decimal.
 
For example if we want to find square root of 5 up to 2 places of decimal then we put 6
[(= 2 � (2 � 1)] zeroes after the decimal place.
 
By doing so, we have 5. 00 00 00. Now we find the square root of 5.00 00 00 in long division method as shown below.
 
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under root 5

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under root of3 4 5 6 7

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under root 5 = 2.236
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