√15-6√6
= $\sqrt[]{9-2.3√6 + 6}$
= $\sqrt[]{(3 - √6)²}$
= 3 - √6
√14-6√5
= $\sqrt[]{(3 - √5)²}$
= 3 - √5
√17-12√2
= 3² - 2.3.2√2 + (2√2)²
= ( 3 - 2√2 )²
√27-12√5
= $\sqrt[]{3.(9-4√5)}$
= $\sqrt[]{3.(√5 - 2)²}$
= (√5 - 2) . √3
= √15 - 2 √3
√4+√15
= $\sqrt[]{8+\frac{2√15}{2}}$
= $\sqrt[]{\frac{(√5 + √3)²}{2}}$
= $\sqrt[]{\frac{2.(√5 + √3)²}{4}}$
= $\frac{√10 + √6}{2}$
