Add 3 root 2 + 7 root 3 and root 2 -5 root 3

1.	Add 3 root 2 + 7 root 3 and root 2 -5 root 3
Answer» To add : $\longrightarrow \sf { (3\sqrt{2} + 7\sqrt{3}) \; \& \; (\sqrt{2}-5\sqrt{3} )} \\$ Answer : $\longrightarrow \sf { 4\sqrt{2} + 2\sqrt{3} }$ Solution : Put the addition sign (+) at the place of and. $\longrightarrow \sf {( 3\sqrt{2} + 7\sqrt{3}) +( \sqrt{2}-5\sqrt{3}) }\\ \\$ Now, removing the brackets. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\longrightarrow \sf { 3\sqrt{2} + 7\sqrt{3}+ \sqrt{2}-5\sqrt{3} }\\ \\$ Grouping the like terms i.e, COLLECT the like terms which has √3 and √2 as common, seperately. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\longrightarrow \sf { 3\sqrt{2}+ \sqrt{2} + 7\sqrt{3} -5\sqrt{3} }\\ \\$ We can see that √2 is common in 3√2 ans 1√2. Also, √3 is common in 7√3 and –5√3. Considering √2 and √3 as common, we can write , ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\longrightarrow \sf { (3+1)\sqrt{2}+ (7-5)\sqrt{3} }\\ \\$ Performing addition and subtraction. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\longrightarrow \sf { (4)\sqrt{2}+ (2)\sqrt{3} }\\ \\$ Removing the brackets. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ $\longrightarrow\boxed { \sf { 4\sqrt{2}+ 2\sqrt{3} }}\\ \\$ Therefore, 4√2 + 2√3 is our required answer. ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ Some RELATED FORMULAE: INDICES identities : • (√a)² = a • √a√b = √ab • √a/√b = √a/b • (√a + √b)(√a - √b) = a - b • (a + √b)(a - √b) = a² - b • (√a ± √b)² = a ± 2√ab + b • (√a + √b)(√c + √d) = √ac + √ad + √bc + √bd

Answer»

To add :

$\longrightarrow \sf { (3\sqrt{2} + 7\sqrt{3}) \; \& \; (\sqrt{2}-5\sqrt{3} )} \\$