Find the square root of 5476 and 1681 and hence find the value of 0.5476 - 0.1681 0.5476 + 0.1681 .

Given number 5476 and 1681 . Let us find 5476 by long division method: 7 4 7 54 ¯ 76 ¯ 49 144 5 76 5 76 0 ∴ 5476 = 74 Now let us find 1681 by long division method: 4 1 2 16 ¯ 81 ¯ 16 81 81 81 0 ∴ 1681 = 41 Solving the value of the expression, we get 0 .5476 - 0 .1681 0 .5476 + 0 .1681 = 0 . 74 - 0 . 41 0 . 74 + 0 . 41 = 0 . 33 0 . 115 = 33 115

Find the square root of 5476 and 1681 and hence find the value of 0.5476 - 0.1681 0.5476 + 0.1681 .

Given number 5476 and 1681 . Let us find 5476 by long division method: 7 4 7 54 ¯ 76 ¯ 49 144 5 76 5 76 0 ∴ 5476 = 74 Now let us find 1681 by long division method: 4 1 2 16 ¯ 81 ¯ 16 81 81 81 0 ∴ 1681 = 41 Solving the value of the expression, we get 0 .5476 - 0 .1681 0 .5476 + 0 .1681 = 0 . 74 - 0 . 41 0 . 74 + 0 . 41 = 0 . 33 0 . 115 = 33 115

Simplify and find the value of 5 + 3 5 - 3 correct to 3 significant figures. Find the value of 3 correct to 2 decimal places.

Given 5 + 3 5 - 3 Multiplying the numerator and denominator by 5 + 3 we get, 5 + 3 5 - 3 = 5 + 3 × ( 5 + 3 ) 5 - 3 × ( 5 + 3 ) = ( 5 + 3 ) 2 5 2 - 3 2 = ( 5 + 3 ) 2 22 = ( 5 + 3 ) 2 22 Let us find the value of 3 using long division method. Hence, we get 3 = 1 . 73 Let us now find 22 by long division method. Hence, we get 22 = 4 . 69 Therefore, ( 5 + 3 ) 2 22 = ( 5 + 1 . 73 ) 2 4 . 69 = 6 . 73 4 . 69 = 1 . 43