By MR. DEVIDAS MADHAO MISTARI
M.Sc. (physics)
Material science
Introduction :
A number is a square root that, when multiplied by itself, corresponds to the desired value. So, for example, the square root of x = 64 is 8 ( 8x8 = 64 ). Squaring is the act of multiplying a number by itself.
[ Using square root symbol : √(x) ] where, x is number.
Method of using the table of square roots (from 1 to10 ) : this table is also known as the table of square roots . At intervals of 0.1, we can find the values of square roots ranging from 1.0 to 9.9.
The table of square roots is essentially divided into the following parts (three parts) , as shown in the following tables.
(i) the number in the table's extreme left vertical column are from 1.1 to 9.9 at intervals of 0.1 .
(ii) at intervals of 1 , the horizontal row at the top of the chart is from 0 to 9.
(iii) at intervals of 1, the number in the horizontal row at the top of the chart are from 1 to 9 .This portion of the chart is referred to as the mean difference column.
* NOTE : The power of 10 extracted under the root sign must always be even number. 10⁻²,10⁻⁴,10² and 10⁴ ⇒ Even power (-2),(-4),(2) and (4)
For Example :
( i ) √(6.479) = ?
SOLUTION : The number in the square roots (from 1 to 10) table extreme left vertical column in 6.4 ,the horizontal row at the top of the chart in 7 consist of containing four digits number 2.544 and horizontal row at the top of the chart in number 9 consist of containing one digit number 2 = 0.002 (mean difference add)·
√(6.479) = ( 2.544 + 0.002 ) = 2.546 (·.·1 < 5 < 9 )
Therefore √(6.479) = 2.546 ... Answer
( ii ) √(647.9) = ?
SOLUTION : √(6.479 x 10²) (decimal place changes from 3ʳᵈ number to 2ⁿᵈ number digit right to left and multiply x 10² )
= √(6.479) x 10¹ [ ·.· √(10²) = 10¹ ]
= ( 2.544 + 0.002 ) x 10¹
= 2.546 x 10¹ = 25.46
Therefore √(6.479) = 25.46 ... Answer
( iii ) √(0.06479) = ?
SOLUTION : √(6.479 x 10⁻² ) (decimal place changes from 1ˢᵗ to 2ⁿᵈ left to right and multiply x 10⁻² )
= ( 2.544 + 0.002 ) x 10⁻¹
[·.· √(10⁻²)=10⁻¹]
= 2.546 x 10⁻¹ = 0.2546
( iv ) √(0.0006479) = ?
SOLUTION : √(6.479 x 10⁻⁴) (decimal place changes from 1ˢᵗ to 4ᵗʰ left to right and multiply x10⁻⁴)
= ( 2.544 + 0.002 ) x 10⁻²
[·.· √(10⁻⁴)=10⁻²]
= 2.546 x 10⁻² = 0.02546
Method of using the table of square (from 10 to 99 ): this table is also known as the table of square roots . At intervals of 1, we can find the values of square roots ranging from 10 to 99.
The table of square roots is essentially divided into the following parts, as shown in the following tables.
(i) the number in the table's extreme left vertical column are from 10 to 99 at intervals of 1 .
(ii) at intervals of 1 , the horizontal row at the top of the chart is from 0 to 9.
(iii) at intervals of 1, the number in the horizontal row at the top of the chart are from 1 to 9 .This portion of the chart is referred to as the mean difference column.
2. Square roots (from 1 to 99)
For Example :
( i ) √(64.79) = ?
SOLUTION : √(64.79) = (8.044 + 0.006)
= 8.050 The number in the square roots (from 10 to 99) table extreme left vertical column in 64 ,the horizontal row at the top of the chart in 7 consist of containing four digits number 8.044 and horizontal row at the top of the chart in number 9 consist of containing one digit number 6 = 0.006 (mean difference add)·
Therefore √(64.79) = 8.050
( ii ) √(6479) = ?
SOLUTION : √(64.79 x 10²) (decimal place changes from 4ᵗʰ number to 2ⁿᵈ number digit right to left and multiply x 10² )
= (8.044 + 0.006) x 10¹
[·.· √(10²)=10¹]
= 8.050 x 10¹ = 80.50
( iii ) √(0.6479) = ?
SOLUTION : √(64·79 x 10⁻²) (decimal place changes from 1ˢᵗ to 2ⁿᵈ left to right and multiply x 10⁻² )
= (8.044 + 0.006) x 10⁻¹
[·.· √(10⁻²)=10⁻¹]
= 8.050x 10⁻¹ = 0.8050
( iv ) √(0.006479) = ?
SOLUTION : √(64·79 x 10⁻⁴) (decimal place changes from 1ˢᵗ to 4ᵗʰ right to left and multiply x 10⁻⁴ )
= (8.044 + 0.006) x 10⁻²
[·.· √(10⁻⁴)=10⁻²]
= 8.050 x 10⁻² = 0.08050
