SOLVED EXAMPLES
Ex. 1. 9587? = 7429 – 4358.
Sol let 9587 – X = 7429 – 4358. Then,
9587 – X = 3071 → X = 95 87 – 3071 = 6516
Ex 2. 5793405 x 9999
Sol. 5793405 x 9999= 5793405 x (10000 – 1)
=57934050000 – 5793405
= 57928256595
Ex. 3. 839478 x 625 = 839478 x 5²
Sol = 839478 x 625 = 839478 x 5⁴
= 839478 x (10/2)⁴ = 839478x 10⁴/2⁵
=8394780000/16 = 524673750
Ex.4. 976x 236 +976 x 763=?
Sol. Using distributive law, we get:
976 x 237 + 976+ 763 = 976 x (237 +763)
=976 x 1000 = 976000.
Ex 5. 986 x 307 – 986 x 207 =?
Sol. By distributive law, we get.
986 x 307 -986x 207 =986 x (307 – 207)
= 986 x 100 = 98600
2560000
+ 49
+22400
|
1582449
|
Ex 6. 1607 x 1607 =?
Sol. 1607 x 1607 = (1607)²
= (1600 + 7)²= (1600)² + 7² + 2 x 1600 x 7
= 2560000 + 49 + 22400 = 2582449.
1960016
-11200
|
1948816
|
Ex. 7. 1396 x 1396 =?
Sol. 1396 x 1396 = (1396)²
= (1400 – 4)² = (1400)² + 4² - 2 x 14000x4
= 1960000 + 49- 11200 = 1948816
Ex. 8. (475 x 475 + 125 x 125) = ?
Sol. We have (a² + b²) = ½ [(a + b)² + (a – b )²]
(475)²+ (125)² = 1/2 [(475 + 125)²(475 – 125)²]
=1/2 x 482500 =241250.
[(a² -b²) = (a + b) (a – B)]
|
Ex. 9. (9 x 96 – 204 x 204) = ?
Sol. 796 + 9 – 204 x 204 = (796)² - (204)²
= (796 + 204) (796 – 204)
= (1000 x 593) = 592000.
Ex 10. (387x 387 + 113 x113 + 2 x 387 x 113)=?
Sol. Given exp. = (387)² + (113)² +2x 387 + 113
(a² +b²+ 2ab), where a = 387 and b = 113
= (a +b)² = (387+ 113)²= (500)² = 250000
Ex. 11. (87x 87 + 61- 2 x 87 x 61)= ?
