Simplify: 7 3 10 + 3 - 2 5 6 + 5 - 3 2 15 + 3 2 .

7 3 10 + 3 - 2 5 6 + 5 - 3 2 15 + 3 2 By rationalising the denominator, = 7 3 10 + 3 × 10 - 3 10 - 3 - 2 5 6 + 5 × 6 - 5 6 - 5 - 3 2 15 + 3 2 × 15 - 3 2 15 - 3 2 = 7 3 ( 10 - 3 ) 10 2 - 3 2 - 2 5 ( 6 - 5 ) 6 2 - 5 2 - 3 2 ( 15 - 3 2 ) 15 2 - 3 2 2 ∵ a + b a - b = a 2 - b 2 = 7 3 ( 10 - 3 ) 10 - 3 - 2 5 ( 6 - 5 ) 6 - 5 - 3 2 ( 15 - 3 2 ) 15 - 18 = 3 ( 10 - 3 ) - 2 5 ( 6 - 5 ) + 2 ( 15 - 3 2 ) = 30 - 3 - 2 30 + 10 + 30 - 6 = 2 30 - 9 - 2 30 + 10 = 1

Mark 3.5 on a number line.

Instructions to draw :- 1. First draw a line segment ' A B ' Which is of 3.5 c m . 2. Now extend the line segment to ' C ' so that ' B C ' = 1 c m . 3. Identify the midpoint of A C and mark as O . 4. Draw a semicircle considering O to be its center and O A as its radius. 5. Now draw a line perpendicular to A C such that B D ⊥ A C , which intersects the semicircle at the point D . 6. Then B D = 3.5 . 7. Having B as its center and B D as the radius draw an arc meeting A C extended to E . Then B E = B D = 3.5 .