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in Mathematics by (15.0k points)

Simplify each of the following expressions:

(i) (√5 + √2)2

(ii) (5 - √2) (5 + √2)

1 Answer

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Best answer

(i) (√5 + √2)2

We need to apply the formula (a + b)2 = a2 +2ab + b2 to find value of (√5 + √2)2

(√5 + √2)2 = (√5)2 + 2 x √5 x √2 + (√2)2

= 5 + 2√10 + 2

= 7 + 2√10

Therefore, on simplifying (√5 √2)2, we get 7+2√0.

(ii) (√5 - √2) (√5 + √2)

We need to apply the formula (a - b) (a + b) = a2 - b2 to find value of (√5 + √2)2

(√5 - √2) (√5 + √2) =(√5)2 - (√2)2

= 5 - 2 = 3

Therefore, on simplifying (√5 - √2) (√5 + √2), we get 3.

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