1.

On simplifying (✓5+✓7)2 we get

Answer»

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:

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


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