3√7(1-√7)

5 answers

To simplify this expression, we will use the distributive property.

3√7(1-√7)

= 3√7 - 3(√7)^2

= 3√7 - 3(7)

= 3√7 - 21

Therefore, 3√7(1-√7) simplifies to 3√7 - 21.
(√6+√3)(√2-2)
To simplify this expression, we will use the distributive property and FOIL method.

(√6+√3)(√2-2)

= (√6)(√2) + (√6)(-2) + (√3)(√2) + (√3)(-2)

= √12 - 2√6 + √6√2 - 2√3

= √12 - 2√6 + √12 - 2√3 (since √6√2 = √12)

= 2√12 - 2√6 - 2√3

= 2(√4∙3) - 2(√2∙3) - 2√3 (since 12 = 4∙3 and 6 = 2∙3)

= 2√4∙√3 - 2√2∙√3 - 2√3

= 4√3 - 2√6 - 2√3

= 2√3 - 2√6

Therefore, (√6+√3)(√2-2) simplifies to 2√3 - 2√6.
(√3+√5)^2
To square the expression (√3+√5), we will use the FOIL method.

(√3+√5)^2

= (√3+√5)(√3+√5)

= (√3)^2 + √3√5 + √5√3 + (√5)^2

= 3 + 2√15 + 5

= 8 + 2√15

Therefore, (√3+√5)^2 simplifies to 8 + 2√15.