3√7(1-√7)
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.
To simplify the expression 3√7(1-√7), we can use the distributive property of multiplication. Here are the steps:
Step 1: Distribute the 3√7 to both terms inside the parentheses:
3√7(1) - 3√7(√7)
Step 2: Simplify each term:
3√7 - 3√7√7
Step 3: Simplify the square root of 7 multiplied by itself (√7 * √7 = 7):
3√7 - 3(√7 * √7)
Step 4: Simplify the remaining term:
3√7 - 3(7)
Step 5: Simplify the multiplication term:
3√7 - 21
So, the simplified expression is 3√7 - 21.
To simplify the expression 3√7(1-√7), we can follow these steps:
Step 1: Distribute the outer term (3√7) to both terms inside the parentheses (1 and -√7).
3√7(1) - 3√7(√7)
Step 2: Simplify each term.
3√7 - 3√(7)(7)
Step 3: Simplify the square root term.
3√7 - 3√(49)
Since the square root of 49 is 7, the expression becomes:
3√7 - 3(7)
Step 4: Simplify further.
3√7 - 21
So the final simplified form of the expression 3√7(1-√7) is 3√7 - 21.