Question

Известно, что 2,2<√5<2,3. Оцените значение выражения: а) 5√5 б) -√5 в) 3+√5 г)3-√5

Answer 1

2,2<√5<2,3
5*2,2<5√5<2,3*5
11<5√5<11,5


2,2<√5<2,3
-2,3<-√5<-2,2


2,2<√5<2,3
5,2<3+√5<5,3


-2,3<-√5<-2,2
-2,3+3<3-√5<-2,2+3
0,7<3-√21<0,8

Answer 2

To estimate the values of the given expressions, we'll use the information provided that 2.2 < √5 < 2.3. Let's proceed with the calculations:

a) 5√5: We know that 2.2 < √5 < 2.3, and we can multiply each part of the inequality by 5 to get the estimate for 5√5:

5 * 2.2 < 5 * √5 < 5 * 2.3 11 < 5√5 < 11.5

So, the estimated value of 5√5 is between 11 and 11.5.

b) -√5: Since √5 is positive, the negative value of √5 will be the negative of the upper bound (2.3):

-√5 ≈ -2.3

c) 3 + √5: We add the lower bound of √5 (2.2) to the number 3:

3 + √5 ≈ 3 + 2.2 = 5.2

d) 3 - √5: We subtract the lower bound of √5 (2.2) from the number 3:

3 - √5 ≈ 3 - 2.2 = 0.8

So, the estimated values are: a) 5√5 ≈ between 11 and 11.5 b) -√5 ≈ -2.3 c) 3 + √5 ≈ 5.2 d) 3 - √5 ≈ 0.8