Question

1) 1/√3-√2 2)0,4*(-10)^3-7*(-10)^2+64 3)-0,7*(-10)^4-5*(-10)^3-32 4)1/ 1/36+1/45

Answer 1

1) решение:

2) решение:

3) решение:

Answer 2

Let's simplify each expression step-by-step:

1. 1/√3 - √2

To simplify this expression, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of √3 - √2, which is √3 + √2.

(1/√3 - √2) * (√3 + √2) / (√3 + √2)

Now, using the difference of squares formula (a^2 - b^2 = (a + b)(a - b)), we get:

= (1 - 3) / (√3)^2 - (√2)^2

= -2 / 3 - 2

= -2 / 5

2. 0.4 * (-10)^3 - 7 * (-10)^2 + 64

First, calculate the powers of (-10):

(-10)^3 = -10 * -10 * -10 = -1000 (-10)^2 = -10 * -10 = 100

Now, substitute these values into the expression:

0.4 * (-1000) - 7 * 100 + 64

= -400 - 700 + 64

= -1036

3. -0.7 * (-10)^4 - 5 * (-10)^3 - 32

Again, calculate the powers of (-10):

(-10)^4 = (-10) * (-10) * (-10) * (-10) = 10000 (-10)^3 = -1000

Now, substitute these values into the expression:

-0.7 * 10000 - 5 * (-1000) - 32

= -7000 + 5000 - 32

= -2032

4. 1 / (1/36 + 1/45)

To simplify this expression, find the common denominator for the fractions in the denominator, which is the least common multiple (LCM) of 36 and 45, which is 180.

1 / (1/36 + 1/45)

Now, rewrite each fraction with the common denominator:

= 1 / ((5/180) + (4/180))

Combine the fractions:

= 1 / (9/180)

Now, divide 1 by 9/180:

= 1 * (180/9)

= 20

Therefore, the simplified value of the expression is 20.