Question

On simplifying (✓5+✓7)2 we get

Answer 1

ANSWER:

Case 1 = 12+2√35

Case 2 = 2√5+2√7

GIVEN:

Case 1 = (√5+√7)²

Case 2 = (√5+√7)2

TO FIND:

Simplify the above expression.

SOLUTION:

Case 1

$= ( \sqrt{5} + \sqrt{7} ) {}^{2} \\ = ( \sqrt{5} ) {}^{2} + ( \sqrt{7} ) {}^{2} + 2 \times ( \sqrt{5} \times \sqrt{7} ) \\ = 5 + 7 + 2 \sqrt{5 \times 7} \\ = 12 + 2 \sqrt{35}$

Case 2

$= ( \sqrt{5} + \sqrt{7} ) \times 2 \\ = 2 \times \sqrt{5} + 2 \times \sqrt{7} \\ = 2 \sqrt{5} + 2 \sqrt{7}$

NOTE:

• I have made the possible question regarding this.

Some important formulas:

• (a+b)²= a²+b²+2ab. (used)
• (a-b)²= a²+b²-2ab.
• (a+b)³= a³+b³+3a²b+3ab²
• (a-b)³= a³-b³-3a²b+3ab²

Answer 2

= (V5+ 7)

= (V5)2 +(V7) +2 (V5 x V7)

= 5 + 7+2/5 x 7

= 12 + 2/35

v==√. root by mistake i have written v