Question

Най­ди­те зна­че­ние вы­ра­же­ния а) 4 ⋅√2 + √50 - √18 б) √9 ⋅ ( 2 √3+ √ 12) в) ( √3 - √2 ) ( √ 3 + √ 2 ) сравните 3⋅√7 и 4⋅√5 сокращение а ) 3⋅3√4b-2 --------------- 2√3⋅2 √b -√ 2 освободитесь от корня 2 ----- √7

Answer 1

№1.
4√2  + √50   - √18 = 4√2  + √(5²*2)  - √(3² * 2) = 4√2 + 5√2  - 3√2 = 
= (4 + 5  - 3)√2  = 6√2

√9 *(2√3  + √12) = 3 * (2√3  + √(2²*3) ) = 3*(2√3 + 2√3) = 3 *4√3 = 12√3

(√3  - √2)(√3 + √2) = (√3)²   - (√2)²  =  3  - 2  = 1

№2.
3√7 = √(9*7) = √63
4√5 = √(16*5) = √80
√63 < √80   ⇒   3√7 <  4√5

№3.
условие некорректное

№4.
2/√7  = ( 2 * √7)  / (√7  * √7) = 2√7 / (√7)²  = 2√7 / 7

Answer 2

A) 4√2+√25*2-√9*2
4√2+5√2-3√2=6√2
b) 3(2√3+2√3) =3*6√3=18√3
в ) (3-2) - по квадрату разности и равно 1

Answer 3

а) Let's calculate the expressions one by one:

a) 4⋅√2 + √50 - √18 = 4⋅√2 + √(5⋅10) - √(2⋅9) = 4⋅√2 + √5⋅√10 - √2⋅√9 = 4⋅√2 + √5⋅√(2⋅5) - √2⋅3 = 4⋅√2 + √5⋅2√5 - 3√2 = (4 + 2√5 - 3)√2 = (2√5 + 1)√2

b) √9⋅(2√3 + √12) = 3⋅(2√3 + √(4⋅3)) = 3⋅(2√3 + 2√3) = 3⋅2√3 + 3⋅2√3 = 6√3 + 6√3 = 12√3

c) (√3 - √2)(√3 + √2) = (√3)^2 - (√2)^2 = 3 - 2 = 1

сравните: 3⋅√7 vs. 4⋅√5

To compare these expressions, we need to determine which one is larger. Since both √7 and √5 are positive (as the principal square roots are always positive), we can directly compare 3⋅√7 and 4⋅√5:

3⋅√7 ≈ 7.937 4⋅√5 ≈ 8.947

We can see that 4⋅√5 is larger than 3⋅√7.

сокращение: а) (3⋅3√4b - 2) / (2√3⋅2√b - √2)

First, let's simplify the numerator: 3⋅3√4b - 2

Now, let's simplify the denominator: 2√3⋅2√b - √2 = 2⋅2√(3b) - √2 = 4√(3b) - √2

Now, the expression becomes: (3⋅3√4b - 2) / (4√(3b) - √2)

To rationalize the denominator, we can multiply both the numerator and denominator by the conjugate of the denominator, which is (4√(3b) + √2):

[(3⋅3√4b - 2) / (4√(3b) - √2)] * [(4√(3b) + √2) / (4√(3b) + √2)]

Now, let's simplify the expression further:

Numerator: = (3⋅3√4b - 2) * (4√(3b) + √2) = 12√(3b) + 3√(8b) - 8√(3b) - 2√2 = (12√(3b) - 8√(3b)) + (3√(8b) - 2√2) = 4√(3b) + 3√(8b) - 2√2

Denominator: = (4√(3b) - √2) * (4√(3b) + √2) = 16√(3b)^2 - (√2)^2 = 16(3b) - 2 = 48b - 2

The simplified expression is: (4√(3b) + 3√(8b) - 2√2) / (48b - 2)