Question

А)√54-√72:√3;б) √28+√63-√112;c)√300-√75. помогите

Answer 1

a) √54-√72/√3=√(9*6)-√(72/3)=3√6-√24=3√6-√4*6=3√6-2√6=√6.

б) √28+√63-√112=√(4*7)+√(9*7)-√(16*7)=2√7+3√7-4√7=5√7-4√7=√7.

в) √300-√75=√(100*3)-√(25*3)=10√3-5√3=5√3.

Answer 2

Sure, I'd be happy to help you simplify these expressions involving square roots:

а) √54 - √72 ÷ √3

First, let's simplify the square roots: √54 = √(9 × 6) = 3√6 √72 = √(9 × 8) = 3√8 √3 remains unchanged.

Now, substitute these values back into the expression: √54 - √72 ÷ √3 = 3√6 - (3√8 ÷ √3)

To divide by a square root, you multiply the numerator and denominator by the square root's conjugate. The conjugate of √3 is (√3), so: 3√6 - (3√8 ÷ √3) = 3√6 - (3√8 ÷ √3) × (√3 ÷ √3)

Now, simplify the expression in the parentheses: 3√6 - (3√8 ÷ √3) × (√3 ÷ √3) = 3√6 - (3√(8 × 3) ÷ √(3 × 3))

Further simplification: 3√6 - (3√(8 × 3) ÷ √(3 × 3)) = 3√6 - (3√24 ÷ 3)

Now, cancel out the common factor of 3 in the numerator and denominator: 3√6 - (3√24 ÷ 3) = 3√6 - √24

To simplify further, find a perfect square factor in the remaining square root: √24 = √(4 × 6) = 2√6

Now, substitute this value back into the expression: 3√6 - √24 = 3√6 - 2√6

Finally, combine like terms: 3√6 - 2√6 = √6

So, the simplified form of the expression is √6.

б) √28 + √63 - √112

Let's simplify the square roots: √28 = √(4 × 7) = 2√7 √63 = √(9 × 7) = 3√7 √112 = √(16 × 7) = 4√7

Now, substitute these values back into the expression: √28 + √63 - √112 = 2√7 + 3√7 - 4√7

Combine like terms: 2√7 + 3√7 - 4√7 = (2 + 3 - 4)√7 = 1√7 = √7

So, the simplified form of the expression is √7.

c) √300 - √75

Let's simplify the square roots: √300 = √(100 × 3) = 10√3 √75 = √(25 × 3) = 5√3

Now, substitute these values back into the expression: √300 - √75 = 10√3 - 5√3

Combine like terms: 10√3 - 5√3 = (10 - 5)√3 = 5√3

So, the simplified form of the expression is 5√3.