I need help bad lol.
9. Explain why 38 is an irrational number.
10. Give two numbers whose square roots add up to 5/
Give two numbers whose cube roots add up to 9.
#9. 38 is not an irrational number
√38 is irrational, because 38 is not a perfect square
#10. 2+3 = 5
So, √4 + √9 = 5
do the cube roots in the same way.
So thats the answer to the first part for 10. and the others are 5+4 are 10 ?
Sure! I can help you with both of those questions.
9. To determine whether a number is rational or irrational, we need to know if it can be expressed as a fraction or not. Rational numbers can be expressed as a ratio of two integers, whereas irrational numbers cannot be expressed as a fraction. In the case of 38, we need to check if it can be expressed as a fraction. Since 38 cannot be expressed as a fraction (i.e., it is not the ratio of two integers), it is considered an irrational number.
10. Let's find two numbers whose square roots add up to 5. Let's call the first number x and the second number y. We can write the equations:
√x + √y = 5 and x + y = (5/)^2.
To solve these equations, we need to use a system of equations. First, we square both sides of the first equation to eliminate the square roots:
(√x + √y)^2 = 5^2
x + 2√xy + y = 25
Since we know that x + y = (5/)^2, we can substitute this into the above equation:
(5/)^2 + 2√xy = 25
25/4 + 2√xy = 25
2√xy = 25 - 25/4
2√xy = (100 - 25)/4
2√xy = 75/4
√xy = 75/4 * 1/2
√xy = 75/8
At this point, we cannot determine the actual values of x and y because they depend on the relationship between x and y. However, we have found an equation relating x and y: √xy = 75/8. We can square both sides to eliminate the square root:
xy = (75/8)^2
xy = 5625/64
Therefore, two numbers whose square roots add up to 5/ are any pair of numbers x and y that satisfy the equation xy = 5625/64.
To solve the second part of the question, finding two numbers whose cube roots add up to 9, we use a similar approach:
Let's call the first number x and the second number y. We can write the equations:
∛x + ∛y = 9 and x + y = (9/)^3.
To eliminate the cube roots, we can cube both sides of the first equation:
(∛x + ∛y)^3 = 9^3
x + 3∛xy(x + y) + 3∛xy(x + y) + y = 729
Substituting x + y = (9/)^3, we have:
x + 3∛xy(9/)^3 + 3∛xy(9/)^3 + y = 729
x + 6∛xy(9/)^3 + y = 729
Simplifying this equation further requires using the relationship between x, y, and ∛xy, which we cannot determine without additional information.
Therefore, to find two numbers whose cube roots add up to 9, we need additional information or constraints that can help solve the equation x + 6∛xy(9/)^3 + y = 729.