Question

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

Answer 1

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.

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$\longrightarrow \sf { 3\sqrt{2} + 7\sqrt{3}+ \sqrt{2}-5\sqrt{3} }$

Grouping the like terms i.e, collect the like terms which has √3 and √2 as common, seperately.

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$\longrightarrow \sf { 3\sqrt{2}+ \sqrt{2} + 7\sqrt{3} -5\sqrt{3} }$

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 ,

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$\longrightarrow \sf { (3+1)\sqrt{2}+ (7-5)\sqrt{3} }$

Performing addition and subtraction.

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$\longrightarrow \sf { (4)\sqrt{2}+ (2)\sqrt{3} }$

Removing the brackets.

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$\longrightarrow\boxed { \sf { 4\sqrt{2}+ 2\sqrt{3} }}$

Therefore, 4√2 + 2√3 is our required answer.

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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