Question

Efectuati calculele:
a) (√5-1)² + √20 =
b) (√3 + √2)² - √24 =
c) (√10-3)² + √20 * √18 =
d) (√14-3)² + 2√7 * √18 =
e) 3(√3+1)² - 2(√3-2)² =
f) (√6-√3)² + (√2-1)(√2+1) =

Answer 1

a) ( √5)² - 2√5 + 1 + √20 = 5 - 2√5 + 1 + √2²·5 = 6 - 2√5 + 2√5 = 6
b) ( √3)² + 2√3·√2 +( √2)² - √24 = 3 + 2√6 + 2 - √2³·3 = 5 + 2√6 - 2√6 = 5
c) ( √10)² - 2·3·√10 + 3² + √20· 18 = 10 - 6√10 + 9 + √2²·5·2·3² = 19 - 6√10 +
   + 2·3√10 = 19 - 6√10 + 6√10 = 19
d) (√14)² - 2·3·√14 + 3² + 2√7·18 = 14 - 6√14 + 9 + 2√7·2·3² =
   = 23 - 6√14 + 2·3√14 = 23 - 6√14 + 6√14 = 23
e) 3[( √3)²+ 2√3 + 1] - 2[( √3)² - 4√3 + 2²] = 3( 3 + 2√3 + 1) - 2( 3 - 4√3 + 1) =
     = 3( 4 + 2√3) - 2( 4 - 4√3)
     = 12 + 6√3 - 8 - 8√3 = 4 - 2√3
f) ( √6)² - 2√6·√3 + (√3)² + (√2)² - 1 = 6 - 2√18 + 3 + 2 - 1 = 10 - 2√18 =
   = 10 - 2√2·3² = 10 - 2·3 √2 = 10 - 6√2